The equation of the locus of the point whose distance from y-axis is half the distance from origin is

**A. ** x^{2} + 3y^{2} = 0

**B. ** x^{2} - 3y^{2}
= 0

**C. ** 3x^{2} + y^{2} = 0

**D. ** 3x^{2} - y^{2}
= 0

**Answer : ****Option D**

**Explaination / Solution: **

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Which of the following equation is the locus of
(at^{2}, 2at)

**A. **

**B. **

**C. ** x^{2} + y^{2} = a^{2}

**D. ** y^{2} = 4ax

**Answer : ****Option D**

**Explaination / Solution: **

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Which of the following point lie on the locus of
3x^{2} + 3y^{2} - 8x - 12y + 17 = 0

**A. ** (0, 0)

**B. ** (-2, 3)

**C. ** (1, 2)

**D. ** (0,-1)

**Answer : ****Option C**

**Explaination / Solution: **

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If the point (8,-5)
lies on the locus x^{2}/16 - y^{2}/25 = k,
then the value of k is

**A. ** 0

**B. ** 1

**C. ** 2

**D. ** 3

**Answer : ****Option D**

**Explaination / Solution: **

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Straight line joining the points (2, 3) and (-1, 4) passes through the point (α,β) if

**A. ** α + 2β =7

**B. ** 3α + β =9

**C. ** α + 3β =11

**D. ** 3α + β =11

**Answer : ****Option C**

**Explaination / Solution: **

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The slope of the line which makes an angle 45̊ with the line 3x - y = -5 are

**A. ** 1, -1

**B. ** 1/2, -2

**C. ** 1,1/2

**D. ** 2, -1/2

**Answer : ****Option B**

**Explaination / Solution: **

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Equation of the straight line that forms an isosceles triangle with coordinate axes in the I-quadrant with perimeter 4 + 2√2 is

**A. ** x + y + 2 = 0

**B. ** x + y - 2 = 0

**C. ** x + y - √2 = 0

**D. ** x + y + √2 = 0

**Answer : ****Option B**

**Explaination / Solution: **

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The coordinates of the four vertices of a quadrilateral are (-2,4), (-1,2), (1,2) and (2,4) taken in order.The equation of the line passing through the vertex (-1,2) and dividing the quadrilateral in the equal areas is

**A. ** x+ 1 = 0

**B. ** x + y = 1

**C. ** x + y + 3 = 0

**D. ** x - y + 3 = 0

**Answer : ****Option D**

**Explaination / Solution: **

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The intercepts of the perpendicular bisector of the line segment joining (1, 2) and (3,4) with
coordinate axes are

**A. ** 5, -5

**B. ** 5, 5

**C. ** 5, 3

**D. ** 5, -4

**Answer : ****Option B**

**Explaination / Solution: **

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The equation of the line with slope 2 and the length of the perpendicular from the origin equal to √5 is

**A. ** x + 2y = √5

**B. ** 2x + y = √5

**C. ** 2x + y = 5

**D. ** x + 2y - 5 = 0

**Answer : ****Option C**

**Explaination / Solution: **

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