## Chapter 11: Conic Sections

Q1. Determine the equation of the circle with radius 4 and Centre (-2, 3).

Ans: x^{2} + y^{2}+ 4x – 6y – 3 = 0

Q2. Determine the focus coordinates, the axis of the parabola, the equation of the directrix and the latus rectum length for y^{2} = -8x

Ans: coordinates of the focus = (-a, 0) = (-2, 0)

axis of the parabola is the x-axis.

Equation of directrix, x= a i.e., x = 2

Length of latus rectum = 8

Q3. Determine the equation for the ellipse that satisfies the given conditions: Centre at (0, 0), the major axis on the y-axis and passes through the points (3, 2) and (1, 6).

Ans: (x^{2}/10) + (y^{2}/40) = 1

Q4. Determine the equation of the hyperbola which satisfies the given conditions: Foci (0, ±13), the conjugate axis is of length 24.

Ans: (y^{2}/25)-(x^{2}/144) = 1

Q5. Calculate the equation of the parabola whose focus is (1, -1) and whose vertex is (2,1). Also, find its axis and latus- rectum).

Ans: 4 √ 5