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 PUBLICATION|Exercise Concept applications 1.2|8 Videos

  • COORDINATE SYSYEM

    CENGAGE PUBLICATION|Exercise Concept applications 1.3|10 Videos

  • COORDINATE SYSYEM

    CENGAGE PUBLICATION|Exercise Solved examples|9 Videos

  • COORDINATE SYSTEM

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|2 Videos

  • CROSS PRODUCTS

    CENGAGE PUBLICATION|Exercise DPP 2.2|13 Videos

Similar Questions

Explore conceptually related problems

If the origin is transferred to the point (-3,2) keeping the axes parallel, then the equation 2x-3y+6=0 becomes-

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

What does the equation (a-b)(x^(2)+y^(2))-2abx=0 become when the origin is shifted to the point ((ab)/(a-b),0) without rotation of axes ?

Find the equation of the curve x^2 + y^2 - 3x + 5y - 8 = 0 when the origin is shifted to (1, 2) without changing the direction of axes.

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

If thte equation 3y^(2)+6y-5x-7=0 reduces to the form y ^(2) =ax when the origin is shifted to the point (h,k) without ration, then the value of (h, k) is-

What does the equation 3x^(2)+2xy+3y^(2)-18x-22y+50=0 become if the axis are tranferred to parallel axis through the point (2,3) ?

An equation of a plane parallel to the plane x -2y + 2z -5 = 0 and at a unit distance from the origin is

The equation of a line which makes concentric to the circle x^2+y^2-4x+2y-20=0 and passes through the origin is __

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.