If one of the two straight lines ax^2+2hxy+by^2=0 coincides with one of the Straight lines a'x^2+2h'

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Rajkishor Patra (M.Sc Jadavpur University)
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[ajitsinghmehra]

The base of a triangle passes through a fixed point (alpha, beta ) and its sides are respectively bisected at right angles by the straight line ax2 + 2hxy + bx2 = 0 . Prove that the locus of its vertex is

(a+b) (x2+y2) + 2h(alpha + beta x ) + (a-b)(alpha x - beta y ) = 0

[ajitsinghmehra]

A parallelogram is formed by the pair of straight lines aX square + 2 X square + b square =0 and the straight lines through the point (p, q)parallel to them . show that the equation of the diagonal which does not pass through the origin is (2x-p)(ap+hq) + (2y-q)(bq+hp) =0

Also show that the area of parallelogram is
ap2 +2hpq +bq2 / {2√(h2-ab)}

[ajitsinghmehra]

Sir ee duto question ta dhire suste kore din 🙏