Home
Class 12
MATHS
A double ordinate of the parabola y^(2)...

A double ordinate of the parabola `y^(2) = 4 ax ` is of length 8a . Prove that the lines joining the vertex to its two ends are at right angles .

Text Solution

Verified by Experts

The correct Answer is:
Therefore, `overline(AP)botoverline(AQ)` i.e.., the joining the vertex to the ends of the double ordinate `overline(PNQ)` are at right angles
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CHHAYA PUBLICATION|Exercise M . C. Q|16 Videos

  • PARABOLA

    CHHAYA PUBLICATION|Exercise Very Short Answer Type Qusetions|21 Videos

  • ORDER AND DEGREE OF DIFFERENTIAL EQUATION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (E Assertion - Reasion Type )|2 Videos

  • PERMUTATION AND COMBINATION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams E Assertion -Reason Type|2 Videos

Similar Questions

Explore conceptually related problems

If the length of the double ordinate of a parabola y^2=4ax is 8a.Prove that the line joining the vertex to its two ends are at right angle.

The vertex of the parabola x^(2)+2y=8x-7 is

PQ is a double ordinate of the parabola y^2=4ax Show that thelocus of its point of trisection the chord PQ is 9y^2=4ax .

overline(PQ) is a double ordinate of the parabola y^(2) = 4ax ,find the equation to the locus of its point of trisection .

Prove that the lines joining the ends of latus rectum of the parabola y^(2) = 4ax with the point of intersection of its axis and directrix are at right angles.

bar(PQ) is a double ordinate of the parabola y^2=4ax ,find the equation to the locus of its point of trisection.

PQ is a chord of the parabola y^(2) = 4ax . The ordinate of P is twice that of Q . Prove that the locus of the mid - point of PQ is 5y^(2) = 18 ax

The coordinates of one end of a focal chord of the parabola y^(2) = 4 ax are (at^(2) , 2 at ) .prove that the coordinates of the other end must be ((a)/(t^(2)),-(2a)/(t)) .

Find the area bounded by the parabola y^(2) =4ax and its double ordinate x =b

A chord overline(PQ) of the parabola y^(2) =4ax , subtends a right angle at the vertex , show that the mid point of overline(PQ) lies on the parabola, y^(2) = 2a (x - 4a) .