Help with AS Level maths question

The lines y=1/2 x and y=−1/2 x are tangents to a circle at the points (2,1) and (-2,1).

Find the equation of the circle in the form x^2+y^2+ ax+ by +c =0

Reply 1

mqb2766

Original post by Hannahhmontanna

The lines y=1/2 x and y=−1/2 x are tangents to a circle at the points (2,1) and (-2,1).

Find the equation of the circle in the form x^2+y^2+ ax+ by +c =0

Just find the equation of the circle in the usual form, then expand.

You know that the radii are perpendicular to the tangents, which enables you to get the centres and radius, either with a sketch and a bi tof reasoning or by forming the equations of the lines for the radii and then finding the point of intersection (centre).

(edited 11 months ago)

Reply 2

FesOsorpro

The tangenal line is perpendicular to the line that passes through the center of circle and the point where the line meet the circle.
Hence first you find the equation of the 2 lines that are perpendicular to the tangenal line and passes through that touching point, then find the 2 intersection point of that 2 lines.
That intersection point is then the center of the circle, and the distance between the any of the touching point and the centre is the radius.
Hope this helps. :smile: