Question

A circle is given by x^2+2mx+y^2+2ny=q. assume that the cirecle has two x-intercepts x_1,x_2 and two y-intercepts y_1,y_2. then the ratio of \frac{x_1+x_2}{y_1+y_2} is:

Answer 1

Answer:

$\frac{x_1+x_2}{y_1+y_2} = \frac{m}{n}$

Explanation:

Given a equation of circle:

x² + 2mx + y² + 2ny = q

We need to find the x & y intercept.

In order to find the x-intercept, we will plug the y = 0 in given equation.

x² + 2mx + (0)² + 2n(0) = q

x² + 2mx - q =

Sum of roots (x₁ + x₂) = -2m

Similarly,

In order to find the y-intercept, we plug x = 0

(0)² + 2m(0) + y² + 2ny = q

y² + 2ny - q = 0

Sum of roots (y₁ + y₂) = -2n

Now we find the ratio of (x₁ + x₂) : (y₁ + y₂) = -2m : -2n

(x₁ + x₂) : (y₁ + y₂) = m : n

or

$\frac{x_1+x_2}{y_1+y_2} = \frac{m}{n}$