Question

the focus and the directrix of parabola are(1,2)and2x-3y+1=0.Then the equation of the tangent at the vertex will be

Answer 1

Answer:

Equation of tangent at vertex is line passing through the vertex of parabola and parallel to directrix so slope of tangent is equal to slope of director

Slope of directrix 2 X -3Y +1= 0

Slope of directrix is M1 = 2/3

Tangent has same slope as directrix = 2/3

Now equation of axis is a line passing through the focus and perpendicular to directrix so slope of axis is

M1 * M2 = -1

2/3 * M2 =-1

M2 =-3/2

Now equation of axis is

Y-2= -3/2(x-1)

2Y -4 = -3X+3

-3X - 2Y +7 =0

3X+2Y-7=0

Equation of directrix is

2X -3Y +1 =0

FIND THE Coordinate of intersection of directrix and axis the find vertex.

Vertex is mid point of focus and directrix

Step-by-step explanation: