1

IIT-JEE 1990

Subjective
A line cuts the $$x$$-axis at $$A (7, 0)$$ and the $$y$$-axis at $$B (0, -5)$$. A variable line $$PQ$$ is drawn perpendicular to $$AB$$ cutting the $$x$$axis in $$P$$ and they $$Y$$-axis in $$Q$$. If $$AQ$$ and $$BP$$ intersect at $$R$$, find the locus of R.

Answer

$${x^2} + {y^2} - 7x + 5y = 0$$
2

IIT-JEE 1990

Subjective
Straight lines $$3x + 4y = 5$$ and $$4x - 3y = 15$$ intersect at the point $$A$$. Points $$B$$ and $$C$$ are choosen on these two lines such that $$AB = AC$$. Determine the possible equations of the line $$BC$$ passing through the point $$(1, 2)$$.

Answer

$$x - 7y + 13 = 0$$ or $$7x + y - 9 = 0$$
3

IIT-JEE 1989

Subjective
Let $$ABC$$ be a triangle with $$AB = AC$$. If $$D$$ is the midpoint of $$BC, E$$ is the foot of the perpendicular drawn from $$D$$ to $$AC$$ and $$F$$ the mid-point of $$DE$$, prove that $$AF$$ is perpendicular to $$BE$$.

Answer

Solve it.
4

IIT-JEE 1988

Subjective
Lines$${L_1} = ax + by + c = 0$$ and $${L_2} = lx + my + n = 0$$ intersect at the point $$P$$ and make an angle $$\theta $$ with each other. Find the equation of a line $$L$$ different from $${L_2}$$ which passes through $$P$$ and makes the same angle $$\theta $$ with $${L_1}$$.

Answer

$$\left( {{a^2} + {b^2}} \right)\left( {\ell x + my + n} \right) - 2\left( {a\ell + bm} \right)\left( {ax + by + c} \right) = 0$$

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