What is the center and radius of the circle given by x^2 + y^2 - 6x + 8y - 11 = 0?
Answer and explanation
Correct answer: A. Center (3, -4) and radius 6
- Step 1: Complete the square: (x - 3)^2 - 9 + (y + 4)^2 - 16 - 11 = 0. Step 2. (x - 3)^2 + (y + 4)^2 = 9 + 16 + 11 = 36. Step 3. Center (h, k) = (3, -4); radius r = sqrt(36) = 6. Answer: Center (3, -4) and radius 6. Why not the others: (-3, 4) reverses signs; 36 is r^2.
Practise more Coordinate Geometry, Conics and Vectors.
Free questions with an explanation for every one, and full timed ECAT Pakistan mock tests.
More Coordinate Geometry, Conics and Vectors questions
- What is the perpendicular distance from the point P(2, -3) to the straight line 3x - 4y + 7 = 0?
- What is the eccentricity e of the ellipse given by the equation 9x^2 + 25y^2 = 225?
- If vectors a = 2i + 3j - k and b = i - 2j + 4k, what is the dot product a . b?
- What is the area of a parallelogram spanned by vectors a = 3i + j and b = i + 4j?
- What are the equations of the asymptotes of the hyperbola x^2 / 16 - y^2 / 9 = 1?
- Find the angle between two straight lines with slopes m1 = 2 and m2 = -3.