Home
Class 12
MATHS
Find the equation to which the equation ...

Find the equation to which the equation `x^2+7x y-2y^2+17 x-26 y-60=0` is transformed if the origin is shifted to the point `(2,-3),` the axes remaining parallel to the original axies.

Text Solution

Verified by Experts

The correct Answer is:
`X^2+7XY-2Y^2-4=0`
Here, the new origin is `(2,-3)` Then,
`x=X+2,Y=Y-3`
and the given equation tranforms to
`(X+2)^2+7(X=2)(Y-3)-2(Y-3)-2(Y-3)^2+17(X+2)-26(Y-3)-60=0` or `X^2+7XY-2Y^2-4=0`
Promotional Banner

Topper's Solved these Questions

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise 1.2|8 Videos

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise 1.3|10 Videos

  • COORDINATE SYSYEM

    CENGAGE|Exercise JEE Main Previous Year|6 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

Find the lines whose combined equation is 6x^2+5x y-4y^2+7x+13 y-3=0

Find the equation of the asymptotes of the hyperbola 3x^2+10 x y+8y^2+14 x+22 y+7=0

Find the equation of the asymptotes of the hyperbola 3x^2+10 x y+9y^2+14 x+22 y+7=0

Find the equation of tangent to the circle x^(2) + y^(2) + 2x -3y -8 = 0 at (2,3)

If theta is the angle between the lines given by the equation 6x^2+5x y-4y^2+7x+13 y-3=0 , then find the equation of the line passing through the point of intersection of these lines and making an angle theta with the positive x-axis.

Find the equation of component lines whose combined equation is 6x^(2)+5xy-4y^(2)+7x+13y-3=0 without solving for xor y.

Find the equation of tangents to circle x^(2)+y^(2)-2x+4y-4=0 drawn from point P(2,3).

Find the equation of the normal to y = x^(2) -2x that is parallel to x + 4y -1 = 0

Find the nearest point on the line x - 2y=5 from the origin.

Find the points on the curve x^(2) + y^(2) – 2x – 3 = 0 at which the tangents are parallel to the x-axis.