Home
Class 12
MATHS
PQ is a chord ofthe parabola y^2=4x who...

PQ is a chord ofthe parabola `y^2=4x` whose perpendicular bisector meets the axis at M and the ordinate of the midpoint PQ meets the axis at N. Then the length MN is equal to

Text Solution

Verified by Experts

The correct Answer is:
2
`P-=(t_(1)^(2),2t_(1))andQ-=(t_(2)^(2),2t_(2))`
L is the midpoint of PQ.
`:." "L-=((1)/(2)(t_(1)^(2)+t_(2)^(2)),(t_(1)+t^(2)))`
`"Slope of PQ"=(2)/(t_(1)+t_(2))`
`y-(t_(1)+t_(2))=(-(t_(1)+t_(2)))/(2)(x-(t_(1)^(2)+t_(2)^(2))/(2))`
Putting y = 0, we get
`M-=(2+(t_(1)^(2)+t_(2)^(2))/(2),0)`
`N-=((t_(1)^(2)+t_(2)^(2))/(2),0)`
`:." "MN=OM-ON=2`
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE|Exercise Exercise 5.2|17 Videos

  • PARABOLA

    CENGAGE|Exercise Exercise 5.3|7 Videos

  • PARABOLA

    CENGAGE|Exercise Question Bank|9 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE|Exercise Exercise (Numerical)|5 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE|Exercise Question Bank|4 Videos

Similar Questions

Explore conceptually related problems

The axis of the parabola y^2 = x is the line

AB is a chord of the parabola y^2 = 4ax with its vertex at A. BC is drawn perpendicular to AB meeting the axis at C.The projecton of BC on the axis of the parabola is

The axis of the parabola x^(2)=-4y is ……. .

PQ is a normal chord of the parabola y^2= 4ax at P,A being the vertex of the parabola. Through P a line is drawn parallel to AQ meeting the x-axis in R. Then the length of AR is : (A) equal to the length of the latus rectum (B) equal to the focal distance of the point P (C) equal to the twice of the focal distance of the point P (D) equal to the distance of the point P from the directrix.

The line 4x+3y-12=0 meets the x-axis at the point……….

Let S is the focus of the parabola y^2 = 4ax and X the foot of the directrix, PP' is a double ordinate of the curve and PX meets the curve again in Q. Prove that P'Q passes through focus.

Find the points on y -axis whose perpendicular distance from the line 4x-3y-12=0 is 3.

From any point P on the parabola y^(2)=4ax , perpebdicular PN is drawn on the meeting it at N. Normal at P meets the axis in G. For what value/values of t, the point N divides SG internally in the ratio 1 : 3, where S is the focus ?

Let PQ be a focal chord of the parabola y^2 = 4ax The tangents to the parabola at P and Q meet at a point lying on the line y = 2x + a, a > 0 . Length of chord PQ is

N is the foot of the perpendicular from P on the transverse axis. The tangent to the hyperbola at P meets the transverse axis at T. If O is the center of the hyperbola the OT.ON is equal to: