Equation of a tangent to the parabola y2=12 x which make an angle of 45° with line y=3 x+77 is

Question

Equation of a tangent to the parabola y2=12 x which make an angle of 45° with line y=3 x+77 is (A) 2 x-4 y+3=0 (B) x+2 y+12=0 (C) 4 x+2 y+3=0 (D) 2 x+y-12=0

Tardigrade Admin · Accepted Answer

Let the equation of tangent is y=m x+(a/m) y=m x+(3/m) tan 45°=|(m-3/1+3 m)| ⇒ (m-3/1+3 m)=± 1 ⇒ 4 m-2=0 2 m+4=0 ⇒ m=(1/2) &-2 ∴ equation of tangents y=-2 x-(3/2) y=(1/2) x+6 2 y=-4 x-3 2 y=x+12

Q. Equation of a tangent to the parabola $y^{2} = 12 x$ which make an angle of $4 5^{\circ}$ with line $y = 3 x + 77$ is

$2 x - 4 y + 3 = 0$

$x + 2 y + 12 = 0$

$4 x + 2 y + 3 = 0$

$2 x + y - 12 = 0$

Q. Equation of a tangent to the parabola y2=12x which make an angle of 45∘ with line y=3x+77 is

2x−4y+3=0

x+2y+12=0

4x+2y+3=0

2x+y−12=0

Let the equation of tangent is y=mx+ma​ y=mx+m3​ tan45∘=∣∣​1+3mm−3​∣∣​ ⇒1+3mm−3​=±1 ⇒4m−2=0&2m+4=0 ⇒m=21​&−2 ∴ equation of tangents y=−2x−23​&y=21​x+6 2y=−4x−3&2y=x+12

Q. Equation of a tangent to the parabola $y^{2} = 12 x$ which make an angle of $4 5^{\circ}$ with line $y = 3 x + 77$ is

$2 x - 4 y + 3 = 0$

$x + 2 y + 12 = 0$

$4 x + 2 y + 3 = 0$

$2 x + y - 12 = 0$