AP Inter 2nd Year Mathematics 2B Guess Paper 2025

1

Find the equation of the circle passing through (- 2, 3) having the centre at (0, 0).

2

If the length of the tangent from (5, 4) to the circle x ² + y ² + 2ky = 0 is 1, then find k.

3

Find the angle between the circles given by the equations

x ² + y ² – 12x – 6y + 41 = 0 and x2 + y2 + 4x + 6y – 59 = 0.

4

Find the equation of parabola whose focus is S (1, -7) and vertex is A (1, -2).

5

If the eccentricity of hyperbola is 54, then find the eccentricity of its conjugate hyperbola

6

Find the value of k, if kx + 3y – 1 = 0, 2x + y + 5 = 0 are conjugate lines with respect to the circle x ² + y ² – 2x – 4y – 4 = 0.

7

Find the equation of the circle which passes through the point (0, -3) and intersects the circles given by the equations

x ² + y ² – 6x + 3y + 5 = 0 and x ² + y2 – x – 7y = 0 orthogonally.

8

Find the eccentricity, co-ordinates of foci, length of latus rectum and equations of the directrix of the following ellipse

9x ² + 16y ² – 36x + 32y – 92 = 0.

9

Find the equation of the tangents to 9x ² + 16y ² = 144 which makes equal intercepts on the coordinate axes.

10

Find the equations of tangents to the hyperbola 3x ² – 4y ² = 12 which are

1. Parallel and
2. Perpendicular to line y = x – 7.

11

Show that (1, 2), (3, -4), (5, -6), and (19, 8) four points are concyclic.

12

Find the direct common tangents of the circles

x ² + y ² + 22x – 4y – 100 = 0 and x2 + y2 – 22x + 4y + 100 = 0.

13

Obtain the reduction formula for In = ∫sec ⁿ xdx, n being a positive integer n ≥ 2 and hence deduce the value of ∫sec ⁵ x dx.

14

Solve (1 + y ² ) dx = (tan-1 y – x) dy.

15

If y ¹ , y ² , y ³ are the y-co-ordinates of the vertices of the triangle inscribed in the parabola y2 = 4ax, then show that the area of the triangle 18a/(y1 – y ² ) (y ² – y ³ ) (y ³ – y ¹ ) | square units.