Home
Class 12
MATHS
Let (x,y) be any point on the parabola y...

Let (x,y) be any point on the parabola `y^2 = 4x`. Let P be the point that divides the line segment from (0,0) and (x,y) n the ratio 1:3. Then the locus of P is :

A

`x^(2)=y`

B

`y^(2)=2x`

C

`y^(2)=x`

D

`x^(2)=2y`

Text Solution

Verified by Experts

The correct Answer is:
C
3
Point P(h,k) divides the line segment OR in ratio `1:3`. So, coordinates of point R are (4h,4k).
(Using ratio OP : PR = `1:3` )
Point R lies on the parabola
`:." "(4k)^(2)=4xx4hork^(2)=h`
Hence, locus is `y^(2)=x`.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • PARABOLA

    CENGAGE ENGLISH|Exercise MULTIPLE CORRECT ANSWER TYPE|7 Videos

  • PARABOLA

    CENGAGE ENGLISH|Exercise Single Correct Answer Type|46 Videos

  • PARABOLA

    CENGAGE ENGLISH|Exercise ARCHIVES SINGLE CORRECT ANSWER TYPE|8 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE ENGLISH|Exercise Numberical Value Type|5 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE ENGLISH|Exercise Comprehension|8 Videos

Similar Questions

Explore conceptually related problems

Let O be the vertex and Q be any point on the parabola, x^2=""8y . It the point P divides the line segment OQ internally in the ratio 1 : 3, then the locus of P is : (1) x^2=""y (2) y^2=""x (3) y^2=""2x (4) x^2=""2y

The point P divides the joining of (2,1) and (-3,6) in the ratio 2:3. Doep P lie on the line x - 5y + 15=0 ?

Let (a,b) be a point on the parabola y=4x-x^(2) and is the point nearest to the point A(-1,4) Find (a+b).

The point P divides the join of (2, 1) and (-3, 6) in the ratio 2 : 3. Does P lie on the line x - 5y + 15 = 0 ?

If P is a point on the parabola y^(2)=8x and A is the point (1,0) then the locus of the mid point of the line segment AP is

The angle between tangents to the parabola y^(2)=4x at the points where it intersects with the line x-y -1 =0 is

Let P be a point on x^2 = 4y . The segment joining A (0,-1) and P is divided by point Q in the ratio 1:2, then locus of point Q is

If P is the point (1,0) and Q is any point on the parabola y^(2) = 8x then the locus of mid - point of PQ is

The straight lines joining any point P on the parabola y^2=4a x to the vertex and perpendicular from the focus to the tangent at P intersect at Rdot Then the equation of the locus of R is (a) x^2+2y^2-a x=0 (b) 2x^2+y^2-2a x=0 (c) 2x^2+2y^2-a y=0 (d) 2x^2+y^2-2a y=0

if the line 4x +3y +1=0 meets the parabola y^2=8x then the mid point of the chord is

Home
Profile