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Projection Formula

Q. 23 If the ...

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Q. }23 If the lines }ax^2+2hxy+ay^2=0 and }x+y=7 form a triangle, then the triangle is }(a≠0)

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a x^{2} - 2 h x y - a y^{2} = 0

represents a pair of straight lines forming with

2 x + 3 y = 6

an isosceles right angled triangle at the origin then

12 a^{2} + 5 h^{2} + 5 a + 12 h + 60

a + b = 2 h

then the area of the triangle formed by the lines

a x^{2} + 2 h x y + b y^{2} = 0

x - y + 2

\frac{α (b - a)}{b + a} u n i t

α

Q. If the pair of straight lines

a x^{2} + 2 h x y + b y^{2} = 0

is rotated about the origin through

90^{\circ},

then the equations in the new position is

Q. Find the area of the triangle formed by the lines

a x^{2} + 2 h x y + b y^{2}

l x + m y + n = 0

Q. Show that the orthocentre of the triangle formed by the straight lines

a x^{2} + 2 h x y + b y^{2} = 0

l x + m y = 1

is a point (x', y') such that

\frac{x^{'}}{l} = \frac{y^{'}}{m} = \frac{a + b}{a m^{2} - 2 h l m + b l^{2}} .

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