Exams › JEE Advanced › Maths
From the external point P(3, 4), tangents are drawn to the ellipse x²/9 + y²/4 = 1, touching it at A and B. Find the orthocentre of triangle PAB.
- (11/5, 8/5)
- (5, 8/7)
- (7/5, 25/8)
- (8/25, 7/5)
Correct answer: (11/5, 8/5)
Solution
The chord of contact AB from P(3,4) is 3x/9 + 4y/4 = 1, i.e. x/3 + y = 1. Working out A, B and the triangle's altitudes gives the orthocentre at (11/5, 8/5).
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 →