Home
Class 12
MATHS
If t is veriable paramete, parameter, sh...

If t is veriable paramete, parameter, show that the locus of the point of intersection of the straight lines `(tx)/(a)+(y)/(b)-t = 0` and `(x)/(a) - (ty)/(b) + 1 = 0` represents an ellipse

Text Solution

Verified by Experts

The correct Answer is:
Therefore, the equation to the locus of (h,k) is `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` , which represpents the eqation of the an ellipse .
Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    CHHAYA PUBLICATION|Exercise M . C . Q|20 Videos

  • ELLIPSE

    CHHAYA PUBLICATION|Exercise Very Short Answer Type Qustions|33 Videos

  • DIRECTION COSINES AND DIRECTION RATIOS

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos

  • GENERAL SOLUTIONS OF TRIGNOMETRIC EQUATIONS

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type-|2 Videos

Similar Questions

Explore conceptually related problems

The locus of the point of intersection of the straight lines (x)/(a) + (y)/(b) = k and (x) /(a) - (y)/(b) = 1/k where k is a non-zero real variable is given by

Show that the locus of the point of intersection of the lines (x)/(a)-(y)/(b) = m and m((x)/(a)+(y)/(b)) = 1 , m being a verible parameter is a hyperbola.

The locus of the point of intersection of the straight lines (x)/(a)+(y)/(b)=K and (x)/(a)-(y)/(b)=(1)/(K) , where K is a non - zero real variable, is given by

For the variable t, the locus of the point of intersection of the lines 3 tx - 2y + 6t = 0 and 3x + 2ty - 6 = 0 is _

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

For the variable t, the locus of the points of intersection of lines 3tx-2y+6t=0 and 3x+2ty-6=0 is

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

If t is parameter then the locus of the point P(t,(1)/(2t)) is _

A variable straight line passes through the point of intersection of the straight lines (x)/(a)+(y)/(b)=1 and (x)/(b)+(y)/(a)=1 and intersects the axes at P and Q. Find the locus of midpoint of PQ.

If a + bne 0 , find the coordinates of focus and the length of latus rectum of the parabola y^(2) = 2 mx which passes through the point of intersection of the straight lines (x)/(a)+(y)/(b)=1 and (x)/(b)+(y)/(a)=1 .