Let the equation of a circle and a parabola be $x^{2} + y^{2} - 4 x - 6 = 0$ and $y^{2} = 9 x$ respectively. Then

(1, - 1)

is a point on the common chord of contact

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

the equation of the common chord is

y + 1 = 0

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

the length of the common chord is

6

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

none of these

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

Open in App

Solution

The correct options are
A the length of the common chord is $6$
C $(1, - 1)$ is a point on the common chord of contact
Given parabola and circle are $y^{2} = 9 x$ and $x^{2} + y^{2} - 4 x - 6 = 0$ respectively.
Now solving these, $x^{2} + 9 x - 4 x - 6 = 0 \Rightarrow x^{2} + 5 x - 6 = 0 \Rightarrow (x - 1) (x + 6) = 0 \Rightarrow x = 1, - 6$ but $x < 0$ is not a solution
Thus $x = 1,$ and corresponding $y = 3, - 3$
Hence point of intersection of the parabola and circle are $(1, - 3), (1, 3)$
Hence equation of common chord is given by, $x = 1$
and length of common chord $= 3 - (- 3) = 6$

Suggest Corrections

Similar questions

x^{2} + y^{2} + 2 x + 2 y + 1 = 0, x^{2} + y^{2} + 4 x + 3 y + 2 = 0

x^{2} + y^{2} + 2 x + 2 y + 1 = 0; x^{2} + y^{2} + 4 x + 3 y + 2 = 0

x^{2} - y^{2} - 2 x + 2 y = 0

2 x^{2} - 4 x + 2 y^{2} + 1 = 0

a, L

x^{2} + y^{2} + 2 x + 3 y + 1 = 0

x^{2} + y^{2} + 4 x + 3 y + 2 = 0

x^{2} + y^{2} + 4 x + 1 = 0

x^{2} + y^{2} + 6 x + 2 y + 3 = 0

Join BYJU'S Learning Program