A variable circle is drawn to touch the line $3 x - 4 y = 10$ and also the circle $x^{2} + y^{2} = 1$ extemally the locus of its centre is -

straight line

No worries! We‘ve got your back. Try BYJU‘S free classes today!

circle

No worries! We‘ve got your back. Try BYJU‘S free classes today!

pair of real, distinct straight lines

No worries! We‘ve got your back. Try BYJU‘S free classes today!

parabola

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D parabola
Consider a line $L_{2}$ , 2 units to left of $L_{1}$ and parallel to $L_{1}$ .
Therefore, distance of centre of circle C from $L_{2} = 2 + r$
And, distance of C from origin = $2 + r$
Therefore, locus of C is a parabola.

Suggest Corrections

Similar questions

(1, 2)

x^{2} + y^{2} = 4

2 x + 4 y + 9 = 0

l x + m y + n = 0

x^{2} + y^{2} = 9

3 x + 4 y = k

x^{2} + y^{2} = 16 x

k

Join BYJU'S Learning Program