Question

find the values of a = b if the equation (a-4) x^2+by^2+(b-3)xy+4x+4y-1=0 represents a circle
​

Answer 1

Answer:

For a second degree equation in x and y

ax^2 + 2hxy + by^2 +2gx + 2fy + c= 0

to represent a circle,

a = b and h= 0

For the given equation a=b and a+b-4 = 0 => a=b= 2

Hence the given equation reduces to

2x^2 + 2y^2 - 2x - 2y - 20 = 0

i.e., x^2 + y^2 - x - y - 10 = 0.

This can be written as

(x- 1/2)^2 + (y - 1/2)^2 = {√(21/2)}^2

This is of the form (x-h)^2 + (y-k)^2 = r^2

Hence the radius of the given circle is √(21/2).

657 views

Related Questions

What is the radius of a circle whose 3x+4y-10=0 and 9x+12y+20=0 as tangents at the extremities of diameter?

648 Views

If the equation of a circle in the xy-plane is shown below, what is the radius of the circle X^2 + Y^2 +4x -2y=-1?

576 Views

If 2x^2+2y^2 + kxy + 3x + 5y - 4 = 0 represents the circle, then what is the value of k equal to?

1,389 Views

(X-a) ²+(y+b) (y-b) =0 ,what is the radius of the circle?

863 Views

If ax^2+2hxy+3y^2-6x-12y-12=0 represents a circle, what is the value of a?

2,830 Views

If the power of (1,1) with respect to the circle x^2+u^2-4x+3y+k=0 is 3, then what is k?

526 Views

What is the center and radius of the circle whose equation is given by x2+y2+4y=0x2+y2+4y=0?

984 Views

How do I find out the radius and the center of the circle, ⓩ-ⓘ/ⓩ+ⓘ=⑤?

19 Views

X^2-2ax+y^2-4bx=0. The equation of a circle in the xy-plane with center (2,4) is shown above. What is the radius of the circle?

3,080 Views

What is the center and radius of the circle (x-2) ^2+(y+4) ^ 2=13?

655 Views

How do I find the radius of the circle 2x2+2y2−8x+12y−28=02x2+2y2−8x+12y−28=0?

926 Views

What is the radius of circles passing through (6,2) and the equation of two normals of circle are x+y=6 and x+2y=4?

1,252 Views

What is the centre and radius of the circle whose equation is given by 4x^2+4y^2-3x-8y=1?

631 Views

What can be the radius of the circle which is concentric with x2+y2+6x-10y-2=0 and touching x- axis?

779 Views

What is the answer for this question? A circle with radius 2^1/2 touches the line x+y-z=0 at (1, 1). What is the length of the tangent drawn from the point (1, 2) to the circle?

Step-by-step explanation:

please follow me