WB JEE 2020 | Straight Lines and Pair of Straight Lines Question 40 | Mathematics

WB JEE 2020

MCQ (Single Correct Answer)

-0.25

Let each of the equations x² + 2xy + ay² = 0 and ax² + 2xy + y² = 0 represent two straight lines passing through the origin. If they have a common line, then the other two lines are given by

$$x - y = 0,\,x - 3y = 0$$

$$x + 3y = 0,\,3x + y = 0$$

$$3x + y = 0,\,3x - y = 0$$

$$(3x - 2y) = 0,\,x + y = 0$$

WB JEE 2020

MCQ (Single Correct Answer)

-0.25

A straight line through the origin O meets the parallel lines 4x + 2y = 9 and 2x + y + 6 = 0 at P and Q respectively. The point O divides the segment PQ in the ratio

1 : 2

3 : 4

2 : 1

4 : 3

WB JEE 2020

MCQ (Single Correct Answer)

-0.5

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 at P(a, 0) and the Y-axis at Q(0, b). If AQ and BP intersect at R, the locus of R is

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

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

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

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

WB JEE 2019

MCQ (Single Correct Answer)

-0.25

A variable line passes through a fixed point $$({x_1},{y_1})$$ and meets the axes at A and B. If the rectangle OAPB be completed, the locus of P is, (O being the origin of the system of axes).

$${(y - {y_1})^2} = 4(x - {x_1})$$

$${{{x_1}} \over x} + {{{y_1}} \over y} = 1$$

$${x^2} + {y^2} = x_1^2 + y_{\kern 1pt} ^2$$

$${{{x^2}} \over {2x_1^2}} + {{{y^2}} \over {y_1^2}} = 1$$

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