Identify each of the following equation at a line a circle a

Identify each of the following equation at a line. a circle. a parabola. an ellipie. or a hyperbola. Assume none ore hyperbota Assume none are degenerate. (a) 4y^3 + 8y = -4x^2 - 18x + 23 (b) 4y^2 + 3x - 6y + 9 = 0 (c) 3x^2 - 6x - 5y^2 + 10y + 10 (d) x = 3 sec theta y = 4 tan theta (e) r = 4/3-2 cos theta (f) r = 6/2 cos theta - 3 sin tetha

Solution

1(A) 4y^2+8y=-4x^{2\\:}-18x\\:+23 is circle with centre at (-9/4,-1)

(b)4y^2+8y=-4x^{2\\:}-18x\\:+23 is parabola with vertex at (7/3,2) and focal ength 3/16

(c)3x^2-6x\\:=5y^{2\\:}+5y\\:+10 is right left parabola with (h,k) at (1,-1/2)

(D) r =4/3-2costheta is ellipse

(e)r=6/(2costheta -3 sintheta is line

(f)r =6/2 +3sintheta is hyperbola.

Matching

2-b

3-e

4f

5a

6c

7d

thank you