MEDIUM
12th Andhra Pradesh Board
IMPORTANT
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Three normals are drawn k,0 to the parabola y2=8x one of the normal is the axis and the remaining two normals are perpendicular to each other, then find the value of -k.

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Important Questions on Parabola

MEDIUM
12th Andhra Pradesh Board
IMPORTANT
Intermediate Second Year Mathematics Paper 2B>Chapter 3 - Parabola>Exercise 3(b)>Q II
Show that the locus of point of intersection of perpendicular tangent to the parabola y2=4ax is the directrix x+a=0.
MEDIUM
12th Andhra Pradesh Board
IMPORTANT
Intermediate Second Year Mathematics Paper 2B>Chapter 3 - Parabola>Exercise 3(b)>Q II
Two parabolas have the same vertex and equal length of latus rectum such that their axes are at right angle. Prove that the common tangents touch each at the end of latus rectum.
MEDIUM
12th Andhra Pradesh Board
IMPORTANT
Intermediate Second Year Mathematics Paper 2B>Chapter 3 - Parabola>Exercise 3(b)>Q II
Show that the foot of the perpendicular from focus to the tangent of the parabola y2=4ax lies on the tangent at vertex.
HARD
12th Andhra Pradesh Board
IMPORTANT
Intermediate Second Year Mathematics Paper 2B>Chapter 3 - Parabola>Exercise 3(b)>Q II
Show that the tangent at one extremity of a focal chord of a parabola is parallel to the normal at other extremity.
MEDIUM
12th Andhra Pradesh Board
IMPORTANT
Intermediate Second Year Mathematics Paper 2B>Chapter 3 - Parabola>Exercise 3(b)>Q III
The normal at a point t1 on y2=4ax meets the parabola again in the point t2. Then prove that t1t2+t12+2=0
MEDIUM
12th Andhra Pradesh Board
IMPORTANT
Intermediate Second Year Mathematics Paper 2B>Chapter 3 - Parabola>Exercise 3(b)>Q III
From an external point P tangents are drawn to the parabola y2=4ax and these tangents make angles θ1,θ2 with its axis, such that cotθ1+cotθ2 is a constant 'd'. Then show that all such P lie on a horizontal line.
MEDIUM
12th Andhra Pradesh Board
IMPORTANT
Intermediate Second Year Mathematics Paper 2B>Chapter 3 - Parabola>Exercise 3(b)>Q III
Show that the common tangents to the circle 2x2+2y2=a2 and the parabola y2=4ax intersect at the focus of the parabola y2=-4ax.
HARD
12th Andhra Pradesh Board
IMPORTANT
Intermediate Second Year Mathematics Paper 2B>Chapter 3 - Parabola>Exercise 3(b)>Q III
The sum of the ordinates of two points on y2=4ax is equal to the sum of the ordinates of two other points on the same curve. Show that the chord joining the first two points is parallel to the chord joining the other two points.