Exams › JEE Advanced › Maths
A circle passes through the points (-1, 1), (0, 6) and (5, 5). Find the point(s) on this circle at which the tangent is parallel to the line joining the origin to the centre of the circle.
- (6, 4) and (-2, 2)
- (4, 6) and (-2, 2)
- (6, 4) and (2, -2)
- (5, 5) and (-1, 1)
Correct answer: (6, 4) and (-2, 2)
Solution
The circle is x² + y² - 4x - 6y + 5 = 0 with centre (2, 3). The diameter through the centre perpendicular to OC meets the circle at (6, 4) and (-2, 2), where the tangents are parallel to OC.
Related JEE Advanced Maths questions
- For the circle represented by (x + c)² + y² = a² and the ellipse given as (x - h)² / b² + y² / a² = 1 (where a, b, c, and h are all positive), if they share a tangent that is horizontal, which condition must be satisfied?
- The expression √(x² + (y - 1)²) - √(x² + (y + 1)²) = K describes a hyperbola when:
- When the circle defined by x² + y² = 1 intersects the rectangular hyperbola xy = 1 at four points (x_i, y_i) for i = 1, 2, 3, 4, which of the following is true?
- The line 3x + 4y = 24 meets the x-axis and y-axis at points A and B, respectively, while the line 4x + 3y = 24 intersects at points C and D. The four points A, B, C, and D are located on which type of curve?
- The curve y = f(x), representing a parabola, is tangent to the line y = x at the point where x = 1. Which of the following is true?
- Given (x, y) ∈ R, where x² + y² = 16, we know y = ±√(16 − x²). When x = 0, y equals ±4. For x = ±4, y equals 0. It is observed that no other integer pairs (x, y) satisfy x² + y² = 16. The set R is defined as {(0, 4), (0, −4), (4, 0), (−4, 0)}. What is one value in the domain of R?
⚔️ Practice JEE Advanced Maths free + battle 1v1 →