Find the equations of tangents to the parabola $y^{2} = 12 x$ which make an angle of $45^{\circ}$ with the line $y = 3 x + 7.$

x - 2 y + 12 = 0

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

x + 2 y + 12 = 0

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

4 x + 2 y + 3 = 0

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

4 x - 2 y - 3 = 0

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

Open in App

Solution

The correct options are
A $x - 2 y + 12 = 0$
C $4 x + 2 y + 3 = 0$
$tan (\pm 45^{\circ}) = \frac{M - 3}{1 + 3 M} \Rightarrow M = - 2, \frac{1}{2}$
or $m = 3, t = tan α = tan 45^{\circ} = 1$
$∴ M = \frac{m - t}{1 + m t}$ and $\frac{m + t}{1 - m t}$ or $\frac{1}{2}, - 2$
$x - 2 y + 12 = 0, 4 x + 2 y + 3 = 0$
Ans: A,C

Suggest Corrections

Similar questions

k

x + y + 2 = 0

x - 2 y + k = 0

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

Find the equation of the chord of contact of tangents to the parabola
$y^{2} = 4 x$ from the point $P (3, 4)$ .

y^{2} = 8 x

45^{\circ}

y = 3 x + 5

y^{2} = 4 x

x y = 2

x + 2 y - 3 = 0, 3 x + 4 y - 7 = 0, 2 x + 3 y - 4 = 0, 4 x + 5 y - 6 = 0

Join BYJU'S Learning Program