The equation of an ellipse is 4x2 y2 10y 13 0 Write the e

The equation of an ellipse is 4x^2 + y^2 +10y + 13 = 0. Write the equation in standard form. x^2/4 + (y + 5)^2/3 = 1 x^2/4 + (y + 5)^2/12 = 1 x^2/3 + (y + 5)^2/12 = 1 x^2/12 + (y + 5)^2/3 = 1 Find the equation of the parabola with vertex (1, 5) and focus (1/4, 5). (x - 1)^2 = -3(y - 5) (x - 1)^2 = 3(y - 5) (y - 5)^2 = -3(x - 1) (y - 5)^2 = 3(x - 1)

Solution

4x²+y²+10y+13=0

4(x-0)²+(y²+10y+25-25)+13=0

4(x-0)²+ (y+5)²=12

(x-0)²/3 + (y+5)²/12=1

Correct option is the third option

11. vertex (4,1)   and    focus (1/4,5)

The parabola is of the form

x=(1/4p)(y-k)²+ h

Where vertex (h,k)= (1,5)

Focus= (h+p,k)= (1/4,5)

h+p=1/4

1+p=1/4

p=-3/4

Required equation is x=(1/-3)(y-5)²+1

(y-5)²= -3(x-1)

Correct option is the third option