# Math Help - [SOLVED] eqn of circle

1. ## [SOLVED] eqn of circle

Given that a circle with centre(-1.5,0.5)and radius 5/2(√ 2)
Find the length of the chord 4x-3y-5=0 of the circle.

Thanks

2. Originally Posted by helloying
Given that a circle with centre(-1.5,0.5)and radius 5/2(√ 2)
Find the length of the chord 4x-3y-5=0 of the circle.

Thanks
Plug in the given values into the general equation of a circle:

$\left(x+\frac32\right)^2+\left(y-\frac12 \right)^2=\dfrac{25}2$

Solve the equation of the line for $y = \frac43x-\frac53$

Plug in the term of y into the equation of the circle. Solve the equation for x. You'll get 2 values: $x_1 = 2~\vee~x_2 = -1$

Plug in these values into the equation of the line to get the corresponding values of y: $y_1 = 1~\vee~y_2 = -3$

The line intersects the circle in the points P(2, 1) and Q(-1, -3).

Calculate the length of the chord PQ:

$|\overline{PQ}|=\sqrt{(2-(-1))^2+(1-(-3))^2} = 5$