List of top Questions asked in TS EAMCET- 2025

Let e be the eccentricity of the ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \). If a=5, b=4 and the equation of the normal drawn at one end of the latus rectum that lies in the first quadrant is \(lx+my=27\), then l+m=

By shifting the origin to the point (-1,2) through translation of axes, if $ax^2+2hxy+by^2+2gx+2fy+c=0$ is the transformed equation of $2x'^2-x'y'+y'^2-3x'+4y'-5=0$, then $2(f+g+h) =$

When the coordinate axes are rotated about the origin through an angle $\frac{\pi}{4}$ in the positive direction, the equation $ax^2+2hxy+by^2=c$ is transformed to $25x'^2+9y'^2=225$, then $(a+2h+b-\sqrt{c})^2=$

The radius of the circle having three chords along y-axis, the line $y=x$ and the line $2x+3y=10$ is

Among the chords of the circle $x^2+y^2=75$, the number of chords having their midpoints on the line $x=8$ and having their slopes as integers is

The lines $x-2y+1=0$, $2x-3y-1=0$ and $3x-y+k=0$ are concurrent. The angle between the lines $3x-y+k=0$ and $mx-3y+6=0$ is $45^\circ$. If m is an integer, then $m-k=$

If $2x-3y+5=0$ and $4x-5y+7=0$ are the equations of the normals drawn to a circle and (2,5) is a point on the given circle, then the radius of the circle is

The focal distance of a point (5,5) on the parabola \( x^2-2x-4y+5=0 \) is

For the parabola \(y = x^2 - 3x + 2\), match the items in list-1 to that of the items in list-2.
S is a focus, Z is intersection of axis and directrix, P is one end point of latus rectum, Q is the point on the parabola at which tangent is parallel to X-axis

If L(p,q), q>3 is one end of the latus rectum of the parabola \((y-2)^2 = 3(x-1)\) then the equation of the tangent at L to this parabola is

The radius of a circle $C_1$ is thrice the radius of another circle $C_2$ and the centres of $C_1$ and $C_2$ are (1,2) and (3,-2) respectively. If they cut each other orthogonally and the radius of the circle $C_1$ is 3r, then the equation of the circle with r as radius and (1,-2) as centre is

If the points A(2,3), B(3,2) form a triangle with a variable point \( p(t, t^2) \), where t is a parameter, then the equation of the locus of the centroid of triangle ABC is

If the equations $3x^2+2hxy-3y^2=0$ and $3x^2+2hxy-3y^2+2x-4y+c=0$ represent the four sides of a square, then $\frac{h}{c}= $

If \( l \) is the maximum value of \( -3x^2+4x+1 \) and \( m \) is the minimum value of \( 3x^2+4x+1 \), then the equation of the hyperbola having foci at \( (l,0), (7m,0) \) and eccentricity as 2 is

O(0,0), B(-3,-1), C(-1,-3) are vertices of a triangle OBC. D is a point on OC and E is a point on OB. If the equation of DE is \(2x + 2y + \sqrt{2} = 0\), then the ratio in which the line DE divides the altitude of the triangle OBC is

The centres of all circles passing through the points of intersection of the circles \(x^2 + y^2 + 2x - 2y + 1 = 0\) and \(x^2 + y^2 - 2x + 2y - 2 = 0\) and having radius \(\sqrt{14}\) lie on the curve

The area of the quadrilateral formed by the lines x+2y+3=0, 2x+4y+9=0, x-2y+3=0 and 3x-6y+11=0 is

The tangents drawn from a point (2,-1) touch the circle \(x^2+y^2+4x-2y+1=0\) at the points A and B. If C is the centre of the circle, then the area (in sq. units) of the triangle ABC is

If a line L passing through the point A(-2,4) makes an angle of 60$^\circ$ with the positive direction of X-axis in anti-clockwise direction and B(p,q) lying in the 3$^\text{rd}$ quadrant is a point on L at the distance of 6 units from the point A, then $\sqrt{p^2+q^2-8q} =$

Two circles which touch both the coordinate axes intersect at the points A and B. If A = (1,2), then AB =

The centre of the circle touching the circles $x^2+y^2-4x-6y-12=0$, $x^2+y^2+6x+18y+26=0$ at their point of contact and passing through the point (1,-1) is

A variable straight-line L with negative slope passes through the point (4,9) and cuts the positive coordinate axes in A and B. If O is the origin, then the minimum value of OA + OB is

If \( x-2y=0 \) is a tangent drawn at a point P on the circle \( x^2+y^2-6x+2y+c=0 \), then the distance of the point (6,3) from P is

The locus of the centre of the circle touching the x-axis and passing through the point \((-1,1)\) is

The power of a point (2,-1) with respect to a circle C of radius 4 is 9. The centre of the circle C lies on the line x+y=0 and in the 2nd quadrant. If \((\alpha, \beta)\) is the centre of the circle C, then \(\beta - \alpha = \)