Question

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

Answer 1

The correct option is B

A Circle

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.