Question

Determine the tangent equation on a parabola $y^{2}$ = -18x parallel to 3x - 2y + 4 = 0

Answer 1

Answer:

y^2 =-18x

3x-2y +4=0 is parallel to tangent

line slope =3/2

Differentiate parabolic eq

2y y'=-18

y'= -9/y

-9/y =3/2

y=-6

Substitute y=-6 in y^2=-18x to get point at which respective tangent is touching parabola

(-6)^2 = -18x

36=-18x

x=-2

So, point at which tangent touching parabola is (-2,-6) having slope 3/2

So, eq of tangent is

y-(-6)= 3/2 ( x-(-2))

y+6 =3/2. ( x+2)

2y+12= 3x+6

2y-3x +6=0

So, 2y -3x +6=0 is tangent on parabola

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