A point moves such that sum of the slopes of the normals drawn from it to the hyperbola
is equal to the sum of ordinates of feet of normals. Prove that the locus of
is a parabola. Find the least distance of this parabola from the circle
Any point on the hyperbola
Now normal at
If the normal passes through
roots of (1) given parameters of feet of normals passing through (h, k).
Let roots be then
From (2) and (3);
Given that Which is a parabola.
Now distance between this parabola and given circle will be along the common normal.
Normal at on the parabola
If it is common normal to parabola and circle, then it passes through the centre (12,0) of circle,
So least distance units.
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