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

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

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 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 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

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

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

The length of the chord of the ellipse $\frac{x^2}{4} + y^2 = 1$ formed on the line $y = x+1$ 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 number of normals that can be drawn through the point (2,0) to the parabola $y^2 = 7x$ is

If $m_1$ and $m_2$ are the slopes of the tangents drawn from the point (1,4) to the parabola $y^2 = 11x$ then $2(m_1^2 + m_2^2) =$

A straight line passing through a point (3,2) cuts X and Y-axes at the points A and B respectively. If a point P divides AB in the ratio 2:3, then the equation of the locus of point P is

If a normal is drawn at a variable point P(x, y) on the curve $9x^2+16y^2-144=0$, then the maximum distance from the centre of the curve to the normal is

If the tangent drawn at the point $P(3\sqrt{2}, 4)$ on the hyperbola $\frac{x^2}{9}-\frac{y^2}{16}=1$ meets its directrix at $Q(\alpha, \beta)$ in the fourth quadrant then $\beta = $

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

Let P be a point on the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ and let the perpendicular drawn through P to the major axis meet its auxiliary circle at Q. If the normals drawn at P and Q to the ellipse and the auxiliary circle respectively meet in R, then the equation of the locus of R is

If $\theta$ is the acute angle between the tangents drawn from the point (1,5) to the parabola $y^2 = 9x$ then

If the normals drawn at the points $P\left(\frac{3}{4}, \frac{3}{2}\right)$ and $Q(3,3)$ on the parabola $y^2 = 3x$ intersect again on $y^2=3x$ at R, then R =

The equation of the locus of a point which is at a distance of 5 units from a fixed point (1,4) and also from a fixed line 2x+3y-1=0 is