Parabolas

[r267747]

I don't know how to solve this question infact i know every formula but i confuse in these questions
So, please solve this question
1)Ques: Find the =n of the parabola whose latus-rectum is 4 units, axis is the line 3x +4y-4=0 amd the tangent at the vertex is the line 4x -3y +7=0
also please draw a diagram for it
I DON'T KNOW HOW TO FIND THE FOCI ,VERTICES, DIRECTRICES, AND AXES OF FOLLOWING PARABOLA
x(square)+2y-3x+5=0

 

[galactus]

The vertex of the parabola lies on the intersection of the the two lines.

\(\displaystyle \frac{-3}{4}x+1=\frac{4}{3}x+\frac{7}{3}\)

Since the latus rectum is 4 units, then p=1. p is the distance from the vertex to the focus and is 1/4th of the length of the latus rectum.

It would appear some rotation is in order. One line is perpendicular to the other. We can see that from the slopes.

Are you studying rotation of axes now?.