Question

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Someone please help me.......❤❤

Find the equation of parabola if the latus rectum joining the points (3,6) and(3,-2)

Answer 1

Hi , Here is your answer !!!

Slope of ( 3,6) and (3,-2 ) is -2-6/ 3-3 = ∞
so latus rectum is perpendicular to axis .


and axis is parallel to X - axis .the equation of the two possible parabola will be of the form

( y - k)² = ±4a( x -h )

latus rectum is distance between point

=> √ (3-3)² + (6+2)² = 8

4a = 8

a = 2

now ,

( y -k )² = ±8(3-h )

point lies on parabola =>

(6-k)² = ±8(3-h) ----------------------1


and

(-2-k)² = ±8(3-h) -----------------------2


from 1 and 2 we get


k = 2


and


from equation 2 we get

16 = ±8(3-h)

h = 3±2



hence the value of h ,k = (5,2) (1,2 )

hence the equation of parabola =>

( y-2)² = 8( x -5 )

and

(y-2)² = -8(x-1)


hope it help you !!!!

thanks !!!

Ranjan kumar ( Ranju )


$thanks$