Question

If the length of a double ordinate is 3.5.and the length from double ordinate to vertex is 3.5 .then what is the length from vertex ro focus?

Answer 1

Double ordinate is perpendicular to axis of parabola hence the ordinates of double ordinate be

P(at2 ,2at ) and P1=(at2 ,-2at)

PP1 = 4a

( (at2 – at2 )^2 + ( 2at+2at) ^2 ) ^1/2 = 4a

( (4at) ^ 2) ^1/2 = 4a

4at = 4a

t = 1;

Hence P = (at2 ,2at ) = ( a,2a)

P1 = ( a, -2a)

Vertex is (0,0)

Slope of OP = m1 = (a-0)/(2a-0) = ½.

Slope of OP1 = m2 = (a-0)/(-2a-0) = -½.

m1 .  m2 = ½ . -1/2

m1 . m2 = -1.

Angle POP1 = 900

Hence  line joining the vertex to ends are at right angles.