List of top Mathematics Questions on Conic sections asked in TS EAMCET

A rectangle is inscribed in the parabola \[ y=9-x^{2} \] such that two of its vertices are on the X-axis and another two on the parabola. The dimensions of such rectangle lying above the X-axis and having maximum area is:

\((1,1)\) is the focus of the parabola \[ y^{2}-4ax-2ay+a^{2}=0. \] If the circles \[ (x-\alpha)^2+(y-\beta)^2=r^2 \] touch the X-axis and the axis of the given parabola, then \[ \{(\alpha,\beta)\} \] is:

The area of the rectangle formed by the tangents drawn at the ends of both major and minor axes of an ellipse is 24. If the eccentricity of the ellipse is \(\frac{1}{4}\), then the equation of the ellipse is:

\(y=4\) is the directrix of the parabola \[ x^{2}+8x+12y+k=0. \] If \(l\) is the length of its latus rectum, then \(l-k=\) ?

The centre of the ellipse lies on the lines \(2x+3y=5\) and \(x+3y=4\). If the eccentricity of the ellipse is \(\frac23\), length of its major axis is 4 and its minor axis is parallel to Y-axis, then the equation of the ellipse is:

For a hyperbola \[ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1, \] the distance between its vertex and focus lying on the positive X-axis is 2. If the length of its latus rectum is 13, then the eccentricity is:

If \(1^\circ \approx 0.01745\) radians, then the approximate value of \[ \sec 29^\circ \] is:

If the eccentricity of the ellipse \[ \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \qquad (a>b) \] is \[ e=\frac{\sqrt3}{2} \] and the equation of one of its directrices is \[ \sqrt3\,x-4=0, \] then \(ab=\):

The area of the quadrilateral formed by the common tangents drawn to the circle \[ x^2+y^2=16 \] and the ellipse \[ 7x^2+25y^2=175 \] is:

If the foci of the ellipse \[ \frac{x^2}{25}+\frac{y^2}{k^2}=1 \qquad (k^2<25) \] and the hyperbola \[ \frac{x^2}{k}-\frac{y^2}{5}=1 \] are the same, then the product of the lengths of the latus rectum of the ellipse and that of the hyperbola is:

The distance of the point \((1,2)\) from the directrix of the parabola \[ y^2-4x-4y+8=0 \] is:

The \(x\)-intercept of one of the common tangents to the circle \[ 3x^2+3y^2=169 \] and the parabola \[ y^2=26x \] is:

Let \(ABC\) be an isosceles triangle. If \(A=(2,3)\), \(B=(3,2)\) and \(BC\) is its base, then the locus of point \(C\) is

If the percentage error in the radius of a circle is 3, then the percentage error in its area is

The number of common tangents that can be drawn to the curves $\frac{x^2}{16}-\frac{y^2}{9}=1$ and $x^2+y^2=16$ is

The ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ ($b>a$) is an ellipse with eccentricity $\frac{1}{\sqrt{2}}$. If the angle of intersection between the ellipse and parabola $y^2=4ax$ is $\theta$, then the coordinates of the point $\frac{20}{3}$ on the ellipse is

The circumcenter of the equilateral triangle having the three points $\theta_1, \theta_2, \theta_3$ lying on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ as its vertices is $(r,s)$. Then the average of $\cos(\theta_1-\theta_2), \cos(\theta_2-\theta_3)$ and $\cos(\theta_3-\theta_1)$ is

The normal at a point on the parabola $y^2=4x$ passes through a point P. Two more normals to this parabola also pass through P. If the centroid of the triangle formed by the feet of these three normals is G(2,0), then the abscissa of P is

If the angle between the tangents drawn to the parabola $y^2=4x$ from the points on the line $4x-y=0$ is $\frac{\pi}{3}$, then the sum of the abscissae of all such points is

A(2,0), B(0,2), C(-2,0) are three points. Let a, b, c be the perpendicular distances from a variable point P on to the lines AB, BC and CA respectively. If a, b, c are in arithmetic progression, then the locus of P is

If the point P($x_1, y_1$) lying on the curve $y = x^2-x+1$ is the closest point to the line $y = x-3$ then the perpendicular distance from P to the line $3x+4y-2=0$ is

Let P, Q, R, S be the points of intersection of the circle $x^2 + y^2 = 4$ and the hyperbola $xy = \sqrt{3}$. If P = $(\alpha,\beta)$ and $\alpha>\beta>0$, then the equation of the tangent drawn at P to the hyperbola is

The length of the chord of the ellipse $\frac{x^2}{4} + y^2 = 1$ formed on the line $y = x+1$ is

If the perpendicular distance from the focus of an ellipse $\frac{x^2}{9} + \frac{y^2}{b^2} = 1$ ($b<3$) to its corresponding directrix is $\frac{4}{\sqrt{5}}$, then the slope of the tangent to this ellipse drawn at $(\frac{3}{\sqrt{2}}, \frac{b}{\sqrt{2}})$ is