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1

### IIT-JEE 1979

Subjective
(a) Two vertices of a triangle are $$(5, -1)$$ and $$(-2, 3).$$ If the orthocentre of the triangle is the origin, find the coordinates of the third point.
(b) Find the equation of the line which bisects the obtuse angle between the lines $$x - 2y + 4 = 0$$ and $$4x - 3y + 2 = 0$$.

(a) $$(-4, -7)$$
(b) $$\left( {4 - \sqrt 5 } \right)x + \left( {2\sqrt 5 - 3} \right)y - \left( {4\sqrt 5 - 2} \right) = 0$$
2

### IIT-JEE 1978

Subjective
One side of rectangle lies along the line $$4x + 7y + 5 = 0.$$ Two of its vertices are $$(-3, 1)$$ and $$(1, 1).$$ Find the equations of the other three sides.

$$\matrix{ {4x + 7y - 11 = 0} \cr {7x - 4y - 3 = 0} \cr {7x - 4y + 25 = 0} \cr }$$
3

### IIT-JEE 1978

Subjective
The area of a triangle is $$5$$. Two of its vertices are $$A\left( {2,1} \right)$$ and $$B\left( {3, - 2} \right)$$. The third vertex $$C$$ lies on $$y = x + 3$$. Find $$C$$.

$$\left( {{{ - 3} \over 2},{3 \over 2}} \right)$$ 0r $$\left( {{{ 7} \over 2},{13 \over 2}} \right)$$
4

### IIT-JEE 1978

Subjective
A straight line segment of length $$\ell$$ moves with its ends on two mutually perpendicular lines. Find the locus of the point which divides the line segment in the ratio $$1 : 2$$

$$9{x^2} + 36{y^2} = 4{\ell ^2}$$

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