Home
Class 12
MATHS
Find the position of points P(1,3) w.r.t...

Find the position of points P(1,3) w.r.t. parabolas `y^(2)=4x and x^(2)=8y`.

Text Solution

Verified by Experts

We have parabolas `y^(2)-4x=0andx^(2)-3y=0`.
Let `S^(1)-=y^(2)-4xandS_(2)-=x^(2)-3y`
Now, `S_(1)(1,3)=3^(2)-4(1)gt0`
And `S_(2)(1,3)=1^(2)-3(3)lt0`
Thus, (1,3) lies in the exterior region of the parabola `y^(2)=4x` and interior region of the parabola `x^(2)=3y`.
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 5.10|1 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 5.11|1 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 5.8|1 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise Numberical Value Type|5 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE PUBLICATION|Exercise Comprehension|8 Videos

Similar Questions

Explore conceptually related problems

If the points of intersection of the parabola y^(2) = 4ax and the circle x^(2) + y^(2) + 2gx + 2fy + c = 0 are (x_(1), y_(1)) ,(x_(2) ,y_(2)) ,(x_(3), y_(3)) and (x_(4), y_(4)) respectively , then _

Find the equation of the tangent to the parabola y^(2)=8x at the point (2t^(2),4t) . Hence find the equation of the tangnet to this parabola, perpendicular to x+2y+7=0

What is the length of the focal distance from the point P(x_(1),y_(1)) on the parabola y^(2) =4ax ?

Find the coordinates of points on the parabola y^2=8x whose focal distance is 4.

Find the points of contact Q and R of a tangent from the point P(2,3) on the parabola y^2=4xdot

Find the equation of the tangent to the parabola y^2=4a x at the point (a t^2,\ 2a t) .

Find the focal distance of a point on the parabola x^(2) = 8y if the ordinate of the point be 11 .

Find the equation of the tangents to the parabola 3y^(2)=8x , parallel to the line x-3y=0 .

Prove that the length of the intercept on the normal at the point P(a t^2,2a t) of the parabola y^2=4a x made by the circle described on the line joining the focus and P as diameter is asqrt(1+t^2) .

If the distance of the point (alpha,2) from its chord of contact w.r.t. the parabola y^2=4x is 4, then find the value of alphadot