Class 11

Math

Co-ordinate Geometry

Straight Lines

Given that $A♢B=4A−B$, what is the value of $(3♢2)♢3$?

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If the lines joining the origin and the point of intersection of curves $ax_{2}+2hxy+by_{2}+2gx+0$ and $a_{1}x_{2}+2h_{1}xy+b_{1}y_{2}+2g_{1}x=0$ are mutually perpendicular, then prove that $g(a_{1}+b_{1})=g_{1}(a+b)˙$

If one of the lines denoted by the line pair $ax_{2}+2hxy+by_{2}=0$ bisects the angle between the coordinate axes, then prove that $(a+b)_{2}=4h_{2}$

If one of the lines of $my_{2}+(1−m_{2})xy−mx_{2}=0$ is a bisector of the angle between the lines $xy=0$ , then $m$ is (a)$1$ (b) $2$ (c) $−21 $ (d) $−1$

Find the equation of the lines through the point (3, 2) which make an angle of $45o$with the line $x−2y=3$.

Find the equation of a line drawn perpendicular to the line $4x +6y =1$through the point, where it meets the yaxis

If $x_{2}+2hxy+y_{2}=0$ represents the equation of the straight lines through the origin which make an angle $α$ with the straight line $y+x=0$ (a)$sec2α=h$ $cosα$ (b)$=(2h)(1+h) $ (c)$2sinα$ $=h(1+h) $ (d) $cotα$ $=(h−1)(1+h) $

Find the equation of the line which satisfy the given conditions : Passing through the point $(−1,1)$and $(2,−4)$

If the slope of one of the lines represented by $ax_{2}+2hxy+by_{2}=0$ is the square of the other, then $ha+b +ab8h_{2} =$ (a) 4 (b) 6 (c) 8 (d) none of these