Slope Form of Tangent
Trending Questions
Q. The locus point of intersection of tangents to the parabola y2=4ax, the angle between them being always 45∘
is
is
- x2−y2+6ax−a2=0
- x2−y2−6ax+a2=0
- x2−y2+6ax+a2=0
- x2−y2−6ax−a2=0
Q. The locus point of intersection of tangents to the parabola y2=4ax, the angle between them being always 45∘
is
is
Q.
Equation of circle touching the line |x−2|+|y−3|=4 will be
Q. The tangent and normal to the ellipse 4x2+9x2=36 at a point P on it meets the major axis in Q and R respectively. If QR = 4, then the eccentric angle of P is
Q.
What's the equation of tangent to the parabola y2=4ax having a slope 'm'.
Q. The equation of the tangent to the parabola y2=16x inclined at an angle of 60∘ to the positive x−axis is
- 3x−√3y+4=0
- 3x+√3y+4=0
- 3x−y+4=0
- 3x+y+4=0
Q.
If the equation of the normal is y = mx + c to the parabola y2=4ax, then find the value of 'c' in terms of a and m.
Q. If a tangent to the parabola y2=8x meets the x-axis at T and intersect the tangent at vertex A at P, and the rectangle TAPQ is completed, then the locus of the point Q is
- y2+2x=0
- x2+2y=0
- x2−2y=0
- y2−2x=0
Q. If line y=2x+14 is tangent to y2=4ax then a is equal to
Q. Find the tangent to the parabola y2=8x which makes an angle of 45∘ to the line
2x+y+3=0
2x+y+3=0
- 9x+3y−2=0
- 9x−3y−2=0
- x+3y+6=0
- x−3y−12=0
Q. The common tangent of the two parabolas y2=4x and x2=32y meets the coordinate axes at A, B respectively. The equation of the circumcircle of ΔOAB is
- x2+y2−4x−2y=0
- x2+y2+4x+2y=0
- x2+y2+2x+y=0
- x2+y2−2x−y=0
Q. The triangle formed by the common tangents to the parabola y2=4x and the circle x2+y2+2x=0 is
- an equilateral triangle
- a right angled isosceles triangle
- an isosceles but not right angled triangle
- a scalene triangle
Q. If the line y=mx+c is tangent to the circle x2+y2=5r2 and the parabola y2−4x−2y+4λ+1=0 and point of contact of the tangent with the parabola is (8, 5), then the value of (25r2+λ+2m+c) is
Q. The equation of the common tangent touching the circle (x−3)2+y2=9 and the parabola y2=4x above the X-axis is
- √3y=3x+1
- √3y=−(x+3)
- √3y=x+3
- √3y=−(3x+1)
Q. If the parabolas y2=4x and x2=32y intersect at (16, 8) at an angle θ, then the value of θ is .
- tan−1(35)
- tan−1(53)
- tan−1(45)
- tan−1(54)
Q.
What's the equation of tangent to the parabola y2=4ax having a slope 'm'.
y=mx+am2
y=mx−am2
y=mx+am
y=mx−am
Q. A tangent is drawn to the parabola y2=4x at a point P on the parabola in the first quadrant and another tangent is drawn to the vertex A of the parabola. Let both the tangent meet at a point B, if area of the triangle ABP=32 unit2, then equation of the tangent is
- 4y=x+8
- 2y=x+8
- 4y=x+16
- 4x=y+16
Q. The slope of the line touching both the parabolas y2=4x and x2=−32y is :
- 12
- 32
- 18
- 23
Q.
The coordinates of the point of contact of the tangent to the parabola y2=16x, which is perpendicular to the line 2x−y+5=0 are
(16, 16)
(16, -16)
(1, 4)
(1, -4)