If line lx + my = 1 be a tangent to circle {x^2} + {y^2} = {a^2} , then locus of point (l, m) is

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10-1.Circle and System of Circles

hard

If the line $lx + my = 1$ be a tangent to the circle ${x^2} + {y^2} = {a^2}$, then the locus of the point $(l, m)$ is

A

A straight line

B

A Circle

C

A parabola

D

An ellipse

Solution

(b) If the line $lx + my – 1 = 0$ touches the circle ${x^2} + {y^2} = {a^2}$,

then applying the condition of tangency, we have $ \pm \frac{{l.0 + m.0 – 1}}{{\sqrt {{l^2} + {m^2}} }} = a$

On squaring and simplifying, we get the required locus ${x^2} + {y^2} = \frac{1}{{{a^2}}}$.

Hence it is a circle.

Standard 11

Mathematics

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