First slide

Parabola

Question

Length of the tangent drawn from an end of the
latus rectum of the parabola $y^{2} = 4 a x$ to the circle
of radius a touching externally the parabola at the
vertex is

Moderate

A

$\sqrt{3} a$
B

$2 a$
C

$\sqrt{7} a$
D

$3 a$

Solution

Equation of the circle is $(x + a)^{2} + y^{2} = a^{2}$ and an
end of the Latus rectum of the parabola is $(a, 2 a)$
.Required length is $\sqrt{(a + a)^{2} + (2 a)^{2} - a^{2}} = a \sqrt{7}$

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