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:
$\displaystyle \left(x+\frac32\right)^2+\left(y-\frac12 \right)^2=\dfrac{25}2$
Solve the equation of the line for $\displaystyle y = \frac43x-\frac53$
Plug in the term of y into the equation of the circle. Solve the equation for x. You'll get 2 values: $\displaystyle x_1 = 2~\vee~x_2 = -1$
Plug in these values into the equation of the line to get the corresponding values of y: $\displaystyle y_1 = 1~\vee~y_2 = -3$
The line intersects the circle in the points P(2, 1) and Q(-1, -3).
Calculate the length of the chord PQ:
$\displaystyle |\overline{PQ}|=\sqrt{(2-(-1))^2+(1-(-3))^2} = 5$