Maths-
General
Easy
Question
If the chord of contact of tangents from a point P to the parabola y2 = 4ax touches the parabola x2 = 4by, the locus of P is -
- a circle
- a parabola
- an ellipse
- a hyperbola
Hint:
The equation chord of contact drawn from a point (x1 ,y1 ) to y2 = 4ax is y y1 = 2a(x + x1) and using the condition it touches x2 = 4by compare it with the condition of tangent to parabola and equate the values of m to find the locus of point p.
The correct answer is: a hyperbola
Let Point P be (p, q) then equation of equation chord of contact drawn to y2 = 4ax is y.q = 2a(x +p)
As chord of contact touches of y2 = 4ax the parabola x2 = 4by
which means chord of contact touches of y2 = 4ax the tangent to parabola x2 = 4by
As it touches x2 = 4by, then equation of line the tangent to x2 = 4by is
y.q = 2a(x +p)
comparing equation and get m = and
then
Therefore, the locus of point p is Hyperbola with equation xy =-2ab
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