A line which the positive direction of x-axis is drawn through the point `P(3, 4),` to cut the curve `y^2= 4x` at `Q ` and `R`. Show that the lengths of the segments `PQ` and `PR` are numerical values of the roots of the equation `r^2sin^2theta+4r(2sintheta-costheta)+4=0`

A line which the positive direction of x -axis is drawn through the point P(3,4), to cut the curve y^(2)=4x at Q and R. Show that the lengths of the segments PQ and PR are numerical values of the roots of the equation r^(2)sin^(2)theta+4r(2sin theta-cos theta)+4=0

A line which makes an acute angle theta with the positive direction of the x-axis is drawn through the point P(3,4) to meet the line x=6 at R and y=8 at Sdot Then, (a) P R=3sectheta (b)P S=4cos e ctheta (c)P R=+P S=(2(3sintheta+4costheta_)/(sin2theta) (d)9/((P R)^2)+(16)/((P S)^2)=1

The tangent at A(2,4) on the curve y=x^(3)-2x^(2)+4 cuts the x -axis at T then length of AT is

Tangents are drawn from the point (-1,2) to the parabola y^(2)=4x. These tangents meet the line x=2 at P and Q, then length of PQ is

A tangent to the circle x^(2)+y^(2)=1 through the point (0, 5) cuts the circle x^(2)+y^(2)=4 at P and Q. If the tangents to the circle x^(2)+y^(2)=4 at P and Q meet at R, then the coordinates of R are

From a variable point P a pair of tangent are drawn to the ellipse x^(2)+4y^(2)=4, the points of contact being Q and R. Let the sum of the ordinate of the points Q and R be unity.If the locus of the point P has the equation x^(2)+y^(2)=ky then find k

If the straight line drawn through the point P(sqrt3,2) and making an angle (pi)/(6) with the x-axis meets the line sqrt3x-4y+8=0 at Q, find the length of PQ.

A straight line through the point A(1,1) meets the parallel lines 4x+2y=9&2x+y+6=0 at points P and Q respectively.Then the point A divides the segment PQ in the ratio:

The tangent and normal at the point P(4,4) to the parabola, y^(2) = 4x intersect the x-axis at the points Q and R, respectively. Then the circumcentre of the DeltaPQR is

Let P and Q be the points on the parabola y^(2)=4x so that the line segment PQ subtends right angle If PQ intersects the axis of the parabola at R, then the distance of the vertex from R is