Equation of Tangent in Parametric Form
Trending Questions
Q. The locus of the point of intersection of tangents to the circle x=acosθ, y=asinθ at the points, whose parametric angles differ by π2 is
- a pair of straight lines
- a straight line
- a circle
- None of these
Q. Let S be the circle in the xy-plane defined by the equation x2+y2=4.
Let P be a point on the circle S with both coordinates being positive. Let the tangent to S at P intersect the coordinate axes at the points M and N. Then, the mid-point of the line segment MN must lie on the curve
Let P be a point on the circle S with both coordinates being positive. Let the tangent to S at P intersect the coordinate axes at the points M and N. Then, the mid-point of the line segment MN must lie on the curve
- (x+y)2=3xy
- x2/3+y2/3=24/3
- x2+y2=2xy
- x2+y2=x2y2
Q. The straight line xcosθ+ysinθ=2, will touch the circle x2+y2−2x=0, if
- θ=nπ, n∈Z
- θ=(2n+1)π, n∈Z
- θ=2nπ, n∈Z
- None of these
Q. Let S be the circle in the xy-plane defined by the equation x2+y2=4.
Let P be a point on the circle S with both coordinates being positive. Let the tangent to S at P intersect the coordinate axes at the points M and N. Then, the mid-point of the line segment MN must lie on the curve
Let P be a point on the circle S with both coordinates being positive. Let the tangent to S at P intersect the coordinate axes at the points M and N. Then, the mid-point of the line segment MN must lie on the curve
- (x+y)2=3xy
- x2/3+y2/3=24/3
- x2+y2=2xy
- x2+y2=x2y2
Q.
Let RS be the diameter of the circle x2+y2=1, where S is the point (1, 0). Let P be a variable point (other than R and S) on the circle and tangents to the circle at S and P meet at the point Q. The normal to the circle at P intersects a line drawn through Q parallel to RS at point E. Then, the locus of E passes through the point(s)
(13, 1√3)
(14, 12)
(13, −1√3)
(14, −12)
Q. Let the tangent to y=f(x) at (a, f(a)) has x−intercept (a−2) and f(0)=2. If f(x) is of the form of kepx, then the value of (kp) is
Q. Find the coordinates of the point on the x-axis that is equidistant from P(4, 3, 1) and Q(−2, −6, −2).
- (32, 0, 0)
- (−32, 0, 0)
- (0, −32, 0)
- (0, 32, 0)
Q. The tangents to the curve x=a(θ−sinθ), y=a(1+cosθ) at the points θ=(2k+1)π, k∈z are parallel to
- y=x
- x+y=0
- x=0
- y=0
Q. The straight line xcosθ+ysinθ=2, will touch the circle x2+y2−2x=0, if
- θ=nπ, n∈Z
- θ=(2n+1)π, n∈Z
- θ=2nπ, n∈Z
- None of these
Q. The coordinates of a point on the unit circle subtending an angle of 30∘ at the origin measured from the positive x-axis in the counter-clockwise direction is:
- (12, 12)
- (12, √32)
- (√32, √32)
- (√32, 12)
Q. Let S be the circle in the xy-plane defined by the equation x2+y2=4.
Let P be a point on the circle S with both coordinates being positive. Let the tangent to S at P intersect the coordinate axes at the points M and N. Then, the mid-point of the line segment MN must lie on the curve
Let P be a point on the circle S with both coordinates being positive. Let the tangent to S at P intersect the coordinate axes at the points M and N. Then, the mid-point of the line segment MN must lie on the curve
- (x+y)2=3xy
- x2/3+y2/3=24/3
- x2+y2=2xy
- x2+y2=x2y2
Q. A unit circle with the following P coordinate is given. The value of θ is:
- 30∘
- 60∘
- 45∘
- 75∘
Q. The locus of the point of intersection of tangents to the circle x=acosθ, y=asinθ at the points, whose parametric angles differ by π2 is
- a straight line
- a circle
- a pair of straight lines
- None of these