KC+CET PYQs for Conic sections with Solutions: Practice KCET Previous Year Questions

Updated on - Feb 16, 2026

Conic sections is an important topic in the Mathematics section in KCET exam. Practising this topic will increase your score overall and make your conceptual grip on KCET exam stronger.

This article gives you a full set of KCET PYQs for Conic sections with explanations for effective preparation. Practice of KCET Mathematics PYQs including Conic sections questions regularly will improve accuracy, speed, and confidence in the KCET 2026 exam.

KCET PYQs for Conic sections with Solutions

1.
If the area of the auxiliary circle of the ellipse $\frac {x^2}{a^2}+\frac {y^2}{b^2}=1 (a >\, b)$ is twice the area of the ellipse, then the eccentricity of the ellipse is
- $\frac {1}{\sqrt {3}}$
- $\frac {1}{2}$
- $\frac {1}{\sqrt {2}}$
- $\frac {\sqrt {3}} {2}$
View Solution
2.
If the focii of $\frac {x^2}{16}+\frac{y^2}{4}=1 $ and $\frac {x^2}{a^2}-\frac{y^2}{3}=1 $ coincide, then value of $a$ is
- $1$
- $\frac {1} {\sqrt {3}}$
- $2$
- $\sqrt {3}$
View Solution
3.
If the area of the Ellipse is $\frac{x^2}{25}+\frac{y^2}{\lambda^2}=1$ is 20π square units, then λ is
- ±4
- ±3
- ±2
- ±1
View Solution
4.
A particle moves along the curve $\frac{x^2}{16}+\frac{y^2}{4}=1$. When the rate of change of abscissa is 4 times that of its ordinate, then the quadrant in which the particle lies is
- III or IV
- I or III
- II or III
- II or IV
View Solution
5.
The locus of the point of intersection of the tangents drawn at the ends of a focal chord of the parabola $x^2=-8y$ is _______
- y = 2
- y = -2
- x = 2
- x = -2
View Solution
6.
If the eccentricity of the hyperbola $\frac {x^2}{a^2}-\frac {y^2}{b^2}=1$ is $\frac {5}{4}$ and $2x + 3y -6 = 0$ is a focal chord of the hyperbola, then the length of transverse axis is equal to
- $\frac {12}{5}$
- $\frac {24}{5}$
- $\frac {6}{5}$
- $\frac {5}{24}$
View Solution
7.
Equation of the circle centered at $(4, 3)$ touching the circle $x^2+y^2-1$ externally, is _____
- $x^2 + y^2 + 8x - 6y + 9 = 0$
- $x^2+y^2-8x + 6y + 9 = 0$
- $x^2 + y^2 - 8t - 6y + 9 = 0$
- $x^2 + y^2 + 8x + 6y + 9 = 0$
View Solution
8.
The length of the latus rectum of $ x^2 + 3y^2 = 12 $ is:
- $ \frac{1}{3} $ units
- $ \frac{4}{\sqrt{3}} $ units
- 24 units
- $ \frac{2}{3} $ units
View Solution
9.
The eccentricity of the ellipse $\frac{x^2}{36} + \frac{y^2}{16} = 1$ is
- $\frac{2\sqrt{5}}{6}$
- $\frac{2\sqrt{5}}{4}$
- $\frac{2\sqrt{13}}{6}$
- $\frac{2\sqrt{13}}{4}$
View Solution
10.
The equation of the tangent to the parabola $y^2 = 4x$ inclined at an angle of $\frac{\pi}{4}$ to the $+ve$ direction of $x$-axis is
- x + y - 4 = 0
- x - y + 4 = 0
- x - y - 1 = 0
- x - y + 1 = 0
View Solution
11.
The points $(1, 0), (0, 1), (0, 0) $ and $ (2k, 3k),k \neq 0$ are concyclic if $k$ = _____
- $-\frac {5}{13}$
- $\frac {5}{13}$
- $\frac {1}{5}$
- $-\frac {1}{5}$
View Solution
12.
If the straight line $3x + 4y = k$ touches the circle $x^2 + y^2 = 16x$, then the value of $k$ is
- 16,64
- -16,-64
- -16,64
- 16,-64
View Solution
13.
The equations of the two tangents from $(-5, - 4)$ to the circle $x^2 + y^2 + 4x + 6y + 8 = 0$ are
- $x + 2y+13 = 0, \, \, \, \, \, \, 2x-y + 6 = 0$
- $2x + y + 13 = 0, \, \, \, \, \, \, x-2y = 6$
- $3x + 2y + 23 = 0 \, \, \, \, \, 2x - 3y + 4 = 0$
- $x-7y = 23, \, \, \, \, \, \, 6x+13y = 4$
View Solution
14.
The sum of the reciprocals of focal distances of a focal chord $PQ$ of $y^2 = 4ax$ is
- $\frac {1}{a}$
- $a$
- $2a$
- $\frac {1}{2a}$
View Solution
15.
Two circles centered at $(2, 3) $ and $(5, 6)$ intersect each other. If the radii are equal, the equation of the common chord is ______
- x + y - 8 = 0
- x - y - 8 = 0
- x + y + 1 = 0
- x - y + 1 = 0
View Solution

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KCET PYQs for Conic sections with Solutions: Practice KCET Previous Year Questions

KCET PYQs for Conic sections with Solutions

1.
If the area of the auxiliary circle of the ellipse $\frac {x^2}{a^2}+\frac {y^2}{b^2}=1 (a >\, b)$ is twice the area of the ellipse, then the eccentricity of the ellipse is

2.
If the focii of $\frac {x^2}{16}+\frac{y^2}{4}=1 $ and $\frac {x^2}{a^2}-\frac{y^2}{3}=1 $ coincide, then value of $a$ is

3.
If the area of the Ellipse is \(\frac{x^2}{25}+\frac{y^2}{\lambda^2}=1\) is 20π square units, then λ is

4.
A particle moves along the curve \(\frac{x^2}{16}+\frac{y^2}{4}=1\). When the rate of change of abscissa is 4 times that of its ordinate, then the quadrant in which the particle lies is

5.
The locus of the point of intersection of the tangents drawn at the ends of a focal chord of the parabola $x^2=-8y$ is _______

6.
If the eccentricity of the hyperbola $\frac {x^2}{a^2}-\frac {y^2}{b^2}=1$ is $\frac {5}{4}$ and $2x + 3y -6 = 0$ is a focal chord of the hyperbola, then the length of transverse axis is equal to

7.
Equation of the circle centered at $(4, 3)$ touching the circle $x^2+y^2-1$ externally, is _____

8.
The length of the latus rectum of \( x^2 + 3y^2 = 12 \) is:

9.
The eccentricity of the ellipse $\frac{x^2}{36} + \frac{y^2}{16} = 1$ is

10.
The equation of the tangent to the parabola $y^2 = 4x$ inclined at an angle of $\frac{\pi}{4}$ to the $+ve$ direction of $x$-axis is

11.
The points $(1, 0), (0, 1), (0, 0) $ and $ (2k, 3k),k \neq 0$ are concyclic if $k$ = _____

12.
If the straight line $3x + 4y = k$ touches the circle $x^2 + y^2 = 16x$, then the value of $k$ is

13.
The equations of the two tangents from $(-5, - 4)$ to the circle $x^2 + y^2 + 4x + 6y + 8 = 0$ are

14.
The sum of the reciprocals of focal distances of a focal chord $PQ$ of $y^2 = 4ax$ is

15.
Two circles centered at $(2, 3) $ and $(5, 6)$ intersect each other. If the radii are equal, the equation of the common chord is ______

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KCET PYQs for Conic sections with Solutions

1.If the area of the auxiliary circle of the ellipse $\frac {x^2}{a^2}+\frac {y^2}{b^2}=1 (a >\, b)$ is twice the area of the ellipse, then the eccentricity of the ellipse is

2.If the focii of $\frac {x^2}{16}+\frac{y^2}{4}=1 $ and $\frac {x^2}{a^2}-\frac{y^2}{3}=1 $ coincide, then value of $a$ is

3.If the area of the Ellipse is \(\frac{x^2}{25}+\frac{y^2}{\lambda^2}=1\) is 20π square units, then λ is

4.A particle moves along the curve \(\frac{x^2}{16}+\frac{y^2}{4}=1\). When the rate of change of abscissa is 4 times that of its ordinate, then the quadrant in which the particle lies is

5.The locus of the point of intersection of the tangents drawn at the ends of a focal chord of the parabola $x^2=-8y$ is _______

6.If the eccentricity of the hyperbola $\frac {x^2}{a^2}-\frac {y^2}{b^2}=1$ is $\frac {5}{4}$ and $2x + 3y -6 = 0$ is a focal chord of the hyperbola, then the length of transverse axis is equal to

7.Equation of the circle centered at $(4, 3)$ touching the circle $x^2+y^2-1$ externally, is _____

8.The length of the latus rectum of \( x^2 + 3y^2 = 12 \) is:

9.The eccentricity of the ellipse $\frac{x^2}{36} + \frac{y^2}{16} = 1$ is

10.The equation of the tangent to the parabola $y^2 = 4x$ inclined at an angle of $\frac{\pi}{4}$ to the $+ve$ direction of $x$-axis is

11.The points $(1, 0), (0, 1), (0, 0) $ and $ (2k, 3k),k \neq 0$ are concyclic if $k$ = _____

12.If the straight line $3x + 4y = k$ touches the circle $x^2 + y^2 = 16x$, then the value of $k$ is

13.The equations of the two tangents from $(-5, - 4)$ to the circle $x^2 + y^2 + 4x + 6y + 8 = 0$ are

14.The sum of the reciprocals of focal distances of a focal chord $PQ$ of $y^2 = 4ax$ is

15.Two circles centered at $(2, 3) $ and $(5, 6)$ intersect each other. If the radii are equal, the equation of the common chord is ______

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1.
If the area of the auxiliary circle of the ellipse $\frac {x^2}{a^2}+\frac {y^2}{b^2}=1 (a >\, b)$ is twice the area of the ellipse, then the eccentricity of the ellipse is

2.
If the focii of $\frac {x^2}{16}+\frac{y^2}{4}=1 $ and $\frac {x^2}{a^2}-\frac{y^2}{3}=1 $ coincide, then value of $a$ is

3.
If the area of the Ellipse is \(\frac{x^2}{25}+\frac{y^2}{\lambda^2}=1\) is 20π square units, then λ is

4.
A particle moves along the curve \(\frac{x^2}{16}+\frac{y^2}{4}=1\). When the rate of change of abscissa is 4 times that of its ordinate, then the quadrant in which the particle lies is

5.
The locus of the point of intersection of the tangents drawn at the ends of a focal chord of the parabola $x^2=-8y$ is _______

6.
If the eccentricity of the hyperbola $\frac {x^2}{a^2}-\frac {y^2}{b^2}=1$ is $\frac {5}{4}$ and $2x + 3y -6 = 0$ is a focal chord of the hyperbola, then the length of transverse axis is equal to

7.
Equation of the circle centered at $(4, 3)$ touching the circle $x^2+y^2-1$ externally, is _____

8.
The length of the latus rectum of \( x^2 + 3y^2 = 12 \) is:

9.
The eccentricity of the ellipse $\frac{x^2}{36} + \frac{y^2}{16} = 1$ is

10.
The equation of the tangent to the parabola $y^2 = 4x$ inclined at an angle of $\frac{\pi}{4}$ to the $+ve$ direction of $x$-axis is

11.
The points $(1, 0), (0, 1), (0, 0) $ and $ (2k, 3k),k \neq 0$ are concyclic if $k$ = _____

12.
If the straight line $3x + 4y = k$ touches the circle $x^2 + y^2 = 16x$, then the value of $k$ is

13.
The equations of the two tangents from $(-5, - 4)$ to the circle $x^2 + y^2 + 4x + 6y + 8 = 0$ are

14.
The sum of the reciprocals of focal distances of a focal chord $PQ$ of $y^2 = 4ax$ is

15.
Two circles centered at $(2, 3) $ and $(5, 6)$ intersect each other. If the radii are equal, the equation of the common chord is ______