Home
Class 11
MATHS
Show that the parametric point (2+t^(2),...

Show that the parametric point `(2+t^(2),2t+1)` represents a parabola. Show that its vertex is (2,1).

Text Solution

AI Generated Solution

To show that the parametric point \((2 + t^2, 2t + 1)\) represents a parabola and to find its vertex, we will follow these steps: ### Step 1: Express \(x\) and \(y\) in terms of \(t\) We have: \[ x = 2 + t^2 \] \[ ...
Promotional Banner

Topper's Solved these Questions

  • CONIC SECTION

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Example|3 Videos

  • CONIC SECTION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 11A|37 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATION

    NAGEEN PRAKASHAN ENGLISH|Exercise MISCELLANEOUS EXERCISE|20 Videos

  • INTRODUCTION OF THREE DIMENSIONAL GEOMETRY

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|6 Videos

Similar Questions

Explore conceptually related problems

ML^(-1)T^(-2) represents

Show that the curve whose parametric coordinates are x=t^(2)+t+l,y=t^(2)-t+1 represents a parabola.

Show that the normal at a point (at^2_1, 2at_1) on the parabola y^2 = 4ax cuts the curve again at the point whose parameter t_2 = -t_1 - 2/t_1 .

Find the angle at which normal at point P(a t^2,2a t) to the parabola meets the parabola again at point Qdot

Find the angle at which normal at point P(a t^2,2a t) to the parabola meets the parabola again at point Qdot

If the normals drawn at the points t_(1) and t_(2) on the parabola meet the parabola again at its point t_(3) , then t_(1)t_(2) equals.

The parametric equations x=(2a(1-t^(2)))/(1+t^(2)) and y=(4at)/(1+t^(2)) represents a circle whose radius is

If the point ( at^2,2at ) be the extremity of a focal chord of parabola y^2=4ax then show that the length of the focal chord is a(t+1/t)^2 .

The curve described parametrically by x=t^2+t+1 , and y=t^2-t+1 represents. (a) a pair of straight lines (b) an ellipse (c) a parabola (d) a hyperbola

If the normal to the parabola y^2=4a x at point t_1 cuts the parabola again at point t_2 , then prove that (t_2)^2geq8.