 # Chapter 11 Conic Secrtions

We are familiar with various concepts of lines, now we have to know about conic section. For various sections of cones like circle, ellipse, parabola, hyperbola etc. we need to go through the details of this chapter. The knowledge which we gain through it has great importance. These figures are related to our real life also like the shape of an egg is elliptical. It will be very interesting to know about them. This chapter has topics such as circle, ellipse, parabola, hyperbola, a point, a straight line, a pair of intersecting lines as a degenerate case of a conic section, standard equations of sections of cone.

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### Exercise 1

•  Q1 Find the equation of the circle with centre (0, 2) and radius 2 Ans: The equation of a circle with centre (h, k) and radius r is given as (x­ – h)2 + (y ­– k)2 = r2 It is given that centre (h, k) = (0, 2) and radius (r) = 2. Therefore, the equation of the circle is (x – 0)2 + (y – 2)2 = 22 x2 + y2 + 4 ­– 4 y = 4 x2 + y2 ­– 4y = 0 Q2 Find the equation of the circle with centre (–2, 3) and radius 4 Ans: The equation of a circle with centre (h, k) and radius r is given as (x­ – h)2 + (y ­– k)2 = r2 It is given that centre (h, k) = (–2, 3) and radius (r) = 4. Therefore, the equation of the circle is (x + 2)2 + (y – 3)2 = (4)2 x2 + 4x + 4 + y2 – 6y + 9 = 16 x2 + y2 + 4x – 6y – 3 = 0