# Thread: Solve Linear equation with second degree to get Quadratic eqn

1. ## Solve Linear equation with second degree to get Quadratic eqn

Hi,

How to solve following equation and get a quadratic equation in X or Y

Ellipse equation with centre (h1,k1) ,major axis(a) and minor axis distance (b)
(X-h1)^ 2 / a^2 + (Y-k1)^2 /b^2 = 1 ------------------ I

and

Circle equation with radius R and centre (h2,k2)

(X-h2)^2 + (Y-k2)^2 = R^2 -------------------------II

Rajee

2. Originally Posted by mrajee
Hi,

How to solve following equation and get a quadratic equation in X or Y

Ellipse equation with centre (h1,k1) ,major axis(a) and minor axis distance (b)
(X-h1)^ 2 / a^2 + (Y-k1)^2 /b^2 = 1 ------------------ I

and

Circle equation with radius R and centre (h2,k2)

(X-h2)^2 + (Y-k2)^2 = R^2 -------------------------II

Rajee
What are you asking? You will NOT get a quadratic equation by solving those equations- they are quadratic. And, contrary to your title, there are no linear equations here.

If you do mean "solve following equation" which variable do you want to solve for?

To solve I for X, subtract (Y- Y1)^2/b^2 from both sides to get (X-X1)/a^2= 1- (Y-Y1)^2/b^2. Multiply both sides by a^2 to get (X-X1)^2= a^2(1- (Y-Y1)^2/b^2). Take the square root of both sides to get X- X1= +/- a sqrt(1- (Y-Y1)^2/b^2). Finally add X1 to both sides to get X= X1 +/- a sqrt{1- (Y-Y1)^2/b^2). That is neither a "linear" nor a "quadratic" equation.

To solve it for Y, Do the same thing but keep Y on the left side rather than X.

To solve II for X or Y, pretty much the same thing but easier- you don't have an "a" or "b" to worry about.