class 11

Math

Co-ordinate Geometry

Coordinate Geometry

The common tangents to the circle $x_{2}+y_{2}=2$ and the parabola $y_{2}=8x$ touch the circle at $P,Q$ andthe parabola at $R,S$. Then area of quadrilateral $PQRS$ is

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Point $P(5,−3)$is one of the two points of trisection of the line segment joining the points $A(7,−2)andB(1,−5)$near to $A$. Find the coordinates of the other point of trisection.

Prove that the points (3, 0), (6, 4) and (-1, 3) are the vertices of a right angled isoscelestriangle.

Find the value of K if the point (K,3), (6,-2) and (-3,4) are collinear.

The line $L_{1}:y−x=0$and $L_{2}:2x+y=0$intersect the line $L_{3}:y+2=0$at P and Q respectively. The bisector of the acute angle between $L_{1}$and $L_{2}$intersects $L_{3}$at R.Statement-1 : The ratio $PR:RQ$equals $22 :5 $Statement-2 : In any triangle, bisector of an angle divides the triangle into two similar triangles. Statement-1 is true, Statement-2 is true ; Statement-2 is correct explanation for Statement-1 Statement-1 is true, Statement-2 is true ; Statement-2 is not a correct explanation for Statement-1 Statement-1 is true, Statement-2 is false Statement-1 is false, Statement-2 is true

Find the coordinates of the midpoint of the line segment joining $P(−11,−8)$ and $Q(8,−2)$.

Show that the following points are collinear.$A(−5,1),B(5,5)$ and $C(10,7)$.

A line passes through $(−3,4)$ and the portion of the line intercepted between the coordinate axes is bisected at the point then equation of line is (A) $4x−3y+24=0$ (B) $x−y−7=0$ (C) $3x−4y+25=0$ (D) $3x−4y+24=0$