Home
Class 12
MATHS
Find the locus of the point (t^2-t+1,t^2...

Find the locus of the point `(t^2-t+1,t^2+t+1),t in Rdot`

Text Solution

Verified by Experts

Let `(h,h)-=(t^2-t+1,t^2+t+1)`
or `h=t^2-t+1` and `k=t^2+t+1`
or `k-h=2t`
or `t=(k-h)/(2)`
or `h=((k-h)/(2))^(2)-((k-h)/(2))+1`
The required locus is
`x=((x-y)/(2))^2-((y-x)/(2))+1`
Promotional Banner

Topper's Solved these Questions

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise 1.1|6 Videos

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise 1.2|8 Videos

  • COORDINATE SYSTEM

    CENGAGE|Exercise Multiple Correct Answers Type|2 Videos

  • CROSS PRODUCTS

    CENGAGE|Exercise DPP 2.2|13 Videos

Similar Questions

Explore conceptually related problems

If the locus of the point (4t^(2)-1,8t-2) represents a parabola then the equation of latus rectum is

If the locus of the point (4t^(2)-1,8t-2) represents a parabola then the equation of latusrectum is

The locus of the point x=(t^(2)-1)/(t^(2)+1),y=(2t)/(t^(2)+1)

If t is a parameter , then locus of a point P (a sin^(2) t, 2a sin t ) is

If the locus of the point ((a)/(2)(t+(1)/(t)),(a)/(2)(t-(1)/(t))) represents a conic,then distance between the directrices is

Find the locus of a point whose coordinate are given by x = t+t^(2), y = 2t+1 , where t is variable.

For the variable t, the locus of the points of intersection of lines x-2y=t and x+2y=(1)/(t) is

The locus of the point represented by x = 3 (cos t + sin t ) , y = 2 ( cos t - sin t ) is

If z=2 + t + i sqrt(3-t^2) , where t is real and t^2 lt 3 , show that the modulus of (z+1)/(z-1) is independent of t. Also show that the locus of the points z for different values of t is a circle and finds its centre and radius.