What is the equation of the parabola whose vertex is ( 3 , 1 ) and directrix is 4 x + 3 y = 5 ?
1 Answer
Equation of parabola is
Explanation:
Parabola is the locus of a point which moves so that its distance from a point, called focus, is equal to its distance from a given line, called directrix. Hence, if focus is
We know the directrix, but not the focus. However, vertex is exactly between focus and directrix. As equation of directrix is
Intersection of this line with directrix can be found by solving simultaneous equations
or
or
or
graph{((x-23/5)^2+(y-11/5)^2-0.1)((x-3)^2+(y-1)^2-0.1)(9x^2-24xy+16y^2-190x-80y+625)(4x+3y-5)(3x-4y-5)=0 [-11.75, 28.25, -4.24, 15.76]}