Q1 · hard · AI-verified
The locus of the midpoint of the chord of the parabola y² = 4ax which passes through the point (h, k) is:
- ky = 2a(x + h)
- ky = 2ax + ah
- y = 2a(x - h)/k
- ky = a(2x - h)
Q2 · hard · AI-verified
The equation of the common tangent to the circles x² + y² = 4 and x² + y² - 6x - 8y + 9 = 0 is:
- 3x + 4y ± 10 = 0
- 4x + 3y ± 10 = 0
- x + y ± 5 = 0
- 2x + y ± 5 = 0
Q3 · hard · AI-verified
The equation of the parabola with vertex at (2, 3) and focus at (2, 5) is:
- (y - 3)² = 8(x - 2)
- (x - 2)² = 8(y - 3)
- (x - 2)² = 12(y - 3)
- (x - 2)² = 4(y - 3)
Q4 · hard · AI-verified
The distance from the point (2, -3) to the line 3x - 4y + 12 = 0 is:
- 4
- 5
- 8
- 6
Q5 · hard · AI-verified
Find the equation of the hyperbola with vertices at (±4, 0) and asymptotes y = ±(3/4)x:
- x²/16 - y²/9 = 1
- x²/9 - y²/16 = 1
- x²/16 - y²/12 = 1
- x²/12 - y²/9 = 1