Find the coordinates of the foci of the ellipse represented by

Question

x^2+25y^2-6x-100y+84=0?

A) (3,2 +2 sqt of 6) 

B) (-2,2), (8,2) 
C) (3 + 2 sqt of 6, 2) 
D) (2 + 2 sqt 6, 2) 
Please show how to do it. Thank you.

Answer 1

The equation of ellipse is .

The standard form of equation of ellipse is ,

where (h, k) = center,  major axis length = 2a, minor axis length = 2b and the relation between a, b and c is .

Write the above equation in standard form.

 To change the expressions into a perfect square trinomial add (half the x coefficient)² to each side of the expression

 Here x coefficient = 6. so, (half the x coefficient)² = (6/2)²= 9

and y coefficient = 4. so, (half the y coefficient)² = (4/2)²= 4.

Add 9(1) and 25(4) = 109 to each side.

If the large denominator is under the x term , then the ellipse is horizontal.

There fore Foci = ( h ± c,k)

To find the vlue of c, substitute the values of a =5and b =1in the equation .

Center (h, k) = (3 , 2) and Foci = ( h ± c,k) = 

Foci =

Solution : C is correct choice.