Board of Intermediate Education, Andhra Pradesh

Mathematics Paper-II (B)
(Coordinate Geometry and Calculus)

Time : 3 Hours
Max Marks : 75

Q.1. If x² + y² – 4x + 6y + c = 0 represents a circle with radius ‘6’, find the value of ‘c’.

Q.2. Find the equation of the directix of the parabola 2x² + 7y = 0.

Q.3. Find the eccentricity of the hyperbola x² – 4y² = 4

Q.4. Find the distance between the two points in a plane whose polar coordinates are (2, π/6) (3, π/4)

Q.5. State the Simpson’s rule for Numerical Integration of a function f(x) over the interval [a,b] by dividing [a,b] into n sub-intervals.

Q.6. Find the equations of the tangents shown drawn from (-2,1) to the hyperbola 2x² – 3y² = 6.

Q.7. Find the equation of the pair of tangents drawn from (3,2) to the circle x² + y² – 6x + 4y – 2 = 0

Q.8. Find the equation of the circle passing through the points of intersection of the circles x² + y² – 8x – 6y + 21 = 0, x² + y² – 2x – 15 = 0 and the point (1,2).

Q.9. Find the equation of the circle passing through the origin and coaxial with the circles x² + y² – 6x + 4y – 8 = 0 and x² + y² – 2x + y + 4 = 0.

Q.10. Find the area enclosed by the curves y = 3x and y = 6x – x².