The equation ax 2 + by 2 + 2hxy + 2gx + 2fy + c = 0 represents a circle only if

Mathematics · JEE Main · NTA Exams — Co-ordinate Geometry

1. a = b, h = 0
2. a = b ≠ 0, h = 0
3. a = b ≠ 0, h = 0, g² + f² – c > 0 
4. a = b ≠ 0, h = 0, g² + f² – ac > 0

Answer

(D) a = b ≠ 0, h = 0, g 2 + f 2 – ac > 0

Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.

Related practice questions

• The curve represented by x = 2 (cos t + sin t), y = 5 (cos t – sin t) is
• Equation of the ellipse whose foci are (4, 0) and (–4, 0) and e = 1/3 is
• The equation 16x 2 – 3y 2 – 32x + 12y – 44 = 0 represents a hyperbola
• A hyperbola passes through the point P( 2 , 3 ) and has foci at ( 2,0) . Then the tangent to this hyperbola…
• If the vertices of ΔABC are A(5,0), B(3,4) and C[ 5 , 2 5 ) , then the coordinates of the orthocentre is
• The points A(2a, 4a), B(2a, 6a) and C(2 a+ 3 a, 5 a)(a>0) are the vertices of
• If a circle passes though the point (a, b) and cuts the circle x^ 2 +y^ 2 =4 orthogonally, then the locus of…
• If the distance between the foci and the distance between the directrices of the hyperbola x^ 2 a^ 2 - y^ 2…

More Co-ordinate Geometry questions · Browse all practice questions