[y=x^(2)+2,y=x,x=0" 24"-2x=3],[" थi "241" ig "sin5a=]

Match the following {:("Point, parabola"," ""Polar"),("I".(3,-2)y^(2)=x," "(a)5x-4y+24=0),("II".(2,1)x^(2)=y," "(b)2x-3y-4=0),("III".(-2,3)y^(2)=4x," "(c)4x-y-1=0),("IV".(5,-6)x^(2)=8y," "(c)x+4y+3=0):}

Match the following . {:("Point, parabola"," ""Tangent"),("I".(3,-6)y^(2)=12x," "(a)x+y+1=0),("II".(2,4)y^(2)=8x," "(b)x+y+3=0),("III".(-2,1)x^(2)=4y," "(c)x-y+2=0):}

2x+3y=0 3x+4y=5

Prove that the following lines are concurrent. (i)5x-3y=1 , 2x+3y=23 , 42x+21y=257 (ii) 2x+3y-4=0 , x-5y+7=0 , 6x-17y+24=0

A pair of perpendicular straight lines is drawn through the origin forming with the line 2x+3y=6 an isosceles triangle right-angled at the origin. The equation to the line pair is 5x^2-24 x y-5y^2=0 5x^2-26 x y-5y^2=0 5x^2+24 x y-5y^2=0 5x^2+26 x y-5y^2=0

The normal form of the eqatuion of the line x+sqrt(3y) = 4 is (A) x cos 60^0 + y sin 60^0 = 2 (B) x cos 24^0 - y sin 24^0 - 2 (C) x cos 240^0 + y sin 240^0 - 2 (D) none of these

Area of the parallelogram formed by 2 x^(2)+5 x y+3 y^(2)=0 and 2 x^(2)+5 x y+3 y^(2)+3 x+4 y+1=0 is

A pair of perpendicular straight lines is drawn through the origin forming with the line 2x+3y=6 an isosceles triangle right-angled at the origin. The equation to the line pair is a. 5x^2-24 x y-5y^2=0 b. 5x^2-26 x y-5y^2=0 c. 5x^2+24 x y-5y^2=0 d. 5x^2+26 x y-5y^2=0