Question

find 'a' if (1,2) is a point on the locus y^2=4ax​

Answer 1

Answer:

a = 1

Step-by-step explanation:

To find---> Value of a if ( 1 , 2 ) is a point on the locus y² = 4ax .

Solution---> ATQ, y² = 4ax .............( 1 )

( 1 , 2 ) is a point on the parabola , so point

( 1 , 2 ) satisfiy the equation ( 1 ).

So satisfying the equation ( 1 ) by ( 1 , 2 ) ie putting

x = 1 and y = 2 , we get,

( 2 )² = 4 a ( 1 )

=> 4 = 4a

=> a = 4 / 4

=> a = 1

Addotional information--->

Equation of parabola

y² = 4 ax

1) Coordinate of vertex = ( 0 , 0 )

2) Coordinate of focus = ( a , 0 )

3) Length of latusrectum = 4a

4) Equation of directrix

x = - a

5) Equation of latusrectum

x = a