MEDIUM
JEE Advanced
IMPORTANT
Earn 100

Find the locus of the middle points of chords of the parabola which passes through the focus.

Important Questions on The Parabola (Continued)

MEDIUM
JEE Advanced
IMPORTANT
The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 9 - The Parabola (Continued)>EXAMPLES XXIX>Q 20
Find the locus of the middle point of chord of the parabola y2=4ax which passes through the fixed point h, k.
HARD
JEE Advanced
IMPORTANT
The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 9 - The Parabola (Continued)>EXAMPLES XXIX>Q 21
Find the locus of the middle points of the chords of the parabola which are normal to the curve.
HARD
JEE Advanced
IMPORTANT
The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 9 - The Parabola (Continued)>EXAMPLES XXIX>Q 22
Find the locus of the middle points of the chords of the parabola which subtend a constant angle θ at the vertex.
HARD
JEE Advanced
IMPORTANT
The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 9 - The Parabola (Continued)>EXAMPLES XXIX>Q 23
Find the locus of the middle points of chords of the parabola y2=4ax which are of given length l.
HARD
JEE Advanced
IMPORTANT
The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 9 - The Parabola (Continued)>EXAMPLES XXIX>Q 24
Find the locus of the middle points of chords of the parabola which are such that the normal at their extremities meet on the parabola.
HARD
JEE Advanced
IMPORTANT
The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 9 - The Parabola (Continued)>EXAMPLES XXIX>Q 25
Through each point of the straight line x=my+h a chord of the parabola y2=4ax is drawn, which is bisected at the point. Prove that it always touches the parabola y+2am2=8ax-h.
HARD
JEE Advanced
IMPORTANT
The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 9 - The Parabola (Continued)>EXAMPLES XXIX>Q 26
Two parabolas have the same axis and tangents are drawn to the second from points on the first. Prove that the locus of the middle points of the chords of contact with the second parabola all lie on a fixed parabola.
HARD
JEE Advanced
IMPORTANT
The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 9 - The Parabola (Continued)>EXAMPLES XXIX>Q 27

Prove that the locus of the feet of the perpendicular drawn from the vertex of the parabola y2=4ax upon chords, which subtend an angle 45° at the vertex, is the curve r2-24arcosθ+16a2cos2θ=0. (where r is the perpendicular distance of the chord from the vertex)