Exams › JEE Advanced › Maths
Tangents are drawn to the hyperbola x²/9 - y²/4 = 1 parallel to the straight line 2x - y = 1. Find the points of contact of these tangents on the hyperbola.
- (9/(2*sqrt(2)), 1/sqrt(2)) and (-9/(2*sqrt(2)), -1/sqrt(2))
- (3*sqrt(3), -2*sqrt(2)) and (-3*sqrt(3), 2*sqrt(2))
- (9/(2*sqrt(2)), -1/sqrt(2)) and (-9/(2*sqrt(2)), 1/sqrt(2))
- (3, 2) and (-3, -2)
Correct answer: (9/(2*sqrt(2)), 1/sqrt(2)) and (-9/(2*sqrt(2)), -1/sqrt(2))
Solution
Setting the tangent slope to 2 gives x1 = (9/2) y1; substituting into the hyperbola yields y1 = +/-1/sqrt(2) and x1 = +/-9/(2 sqrt(2)).
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 →