a tangent to the parabola y2=8x makes an angle of 45 degree with the straight line y=3x+5 then what is - Maths - Conic Sections

Question

a tangent to the parabola y2=8x makes an angle of 45 degree with
the straight line y=3x+5 then what is the equation of tangent?

Anuradha Sharma · Accepted Answer

Let the slop of the tangent is m
Now slop of this given line y = 3x+5 is 3 and they are making an angle of 45degree , So tan 45= m-31+3m  From slop formula tan θ=m1-m21+m1m21=m-31+3m Now taking positive sign, m-3=1+3m2m=-4 or m = -2Now taking negative sign we get, m-3=-1-3m4m=2m = 12Now equation of tangent of slop m to the parabola y2=4ax isy = mx+amFormulaHere a = 2 from y2=8x and m are -2 and 1/2 respectively so putting these valuewe get, tangents y = -2x-1 and y = 12x+4

a tangent to the parabola y2=8x makes an angle of 45 degree with the straight line y=3x+5.then what is the equation of tangent?