Question

A variable circle passes through the point (a,b) and touches the x axis ; show that the locus of the diametric end

Answer 1

A variable circle passes through the point A(a,b) and touches the x-axis. Show that the locus of the other end of the diameter through A is (x-a)^2=4by.

Can anyone please help me in this question?

4 years ago

Answers : (1)

Let the other end of the diameter through A be (h,k)

So the coordinated of the center are ()

Now you can calculate the radius of the circle as the coordinates of the centre and one point on the circle are known
Therefore, Radius = 

Now since the circle is touching the x-axis, radius=ordinate of center



Now simplify this and get the required.
Hence proved