List of top Mathematics Questions on Conic sections asked in KCET

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

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

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

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

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

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

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

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

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

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

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

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

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 _______

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

The condition for the line $y = mx +c$ to be a normal to the parabola $y = 4ax$ is _______

For the parabola $y^2 = 4x$, the point $P$ whose focal distance is $17$, is

The tangents drawn at the extremeties of a focal chord of the parabola $y^2 = 16 x$

If the circles $x ^2 + y ^2 =9$ and $x^2 + y^ 2 + 2\alpha x + 2y +1 = 0$ touch each other internally, then $\alpha$ =

If the circles $x^2 + y^2 - 2x - 2y - 7 = 0$ and $x^2 + y^2 + 4x + 2y + k = 0$ cut orthogenally, then the length of the common chord of the circles is

If $\frac {x^2}{36}-\frac{y^2} {k^2} = 1$ is a hyperbola, then which of the following statements can be true ?

If $3x + y + k = 0$ is a tangent to the circle $x^2+y^2=10$ the values of k are,

$x^2 + y^2 -6x-6y + 4 = 0, x^2 + y^2 - 2x - 4y + 3 - 0 , x^2 + y^2 + 2k x + 2y +1 = 0$. If the Radical centre of the above three circles exists, then which of the following cannot be the value of $k$ ?