Home
Class 12
MATHS
Find the equation of the tangent to the ...

Find the equation of the tangent to the circle `x^2+y^2+4x-4y+4=0` which makes equal intercepts on the positive coordinates axes.

Text Solution

Verified by Experts

The correct Answer is:
`x+y=+-2sqrt(2)`
Let the equation of the tangent be
`(x)/(a)+(y)/(a)=1`
i.e., `x+y=a ` (1)
Therefore, the length of perpendicular from the center (-2,2) on (1) is equal to the radius, i.e., `sqrt(4+4-4)` . So,
`(|-2+2-a|)/(sqrt(1+1))=2`
or `a= + 2 sqrt(2)`
Hence, the equations of the tangents are `x+y= +- 2 sqrt(2)`.
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Find the equations of the tangents drawn to the curve y^2-2x^3-4y+8=0.

Find the equation of the tangent to the circle x^2 + y^2 - 2ax - 2ay + a^2 = 0 which makes with the coordinate axes a triangle of area a^2.

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

Find the equations of the tangents to the circle x^2+y^2-6x+4y=12 which are parallel to the straight line 4x+3y+5=0

Find the equations of tangents to the circle x^2+y^2-22 x-4y+25=0 which are perpendicular to the line 5x+12 y+8=0

The equation of the tangent to the circle x^2+y^2=a^2, which makes a triangle of area a^2 with the coordinate axes, is x+-y=asqrt(2) (b) x+-y=+-asqrt(2) x+-y=2a (d) x+y=+-2a

Find the equation of tangents to the curve 4x^2-9y^2=1 which are parallel to 4y=5x+7.

Find the equation of the tangent and normal to the circle x^(2)+y^(2)=25 at P(-3,4)

Find the equation of tangents to hyperbola x^(2)-y^(2)-4x-2y=0 having slope 2.

If a chord of a the circle x^(2)+y^(2) = 32 makes equal intercepts of length of l on the co-ordinate axes, then