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Co Ordinate Geometry - Mathematics Questions asked by Filo students

Question 1

A (1, 2)

and

B (7, 10)

are two points. If

P (x)

is a point such tnat (are) true? of the triangle APB is maximum, then which of

P lies on the straight line $3 x + 4 y = 36$
P lies on any line perpendicular
$P$ lies on the circle passing through the points $(1, 2)$ and $(7, 10)$ and having a radius of 10 units

Topic:

Coordinate Geometry

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Question 2

A, B

then find the locus of

P

. (MARCH-2009, 2006) (TS MAR 15) 1)

O (0, 0), A (6, 0)

and

B (0, 4)

are three points. If

P

is a point such that the area of

△ POB

is twice the area of

△ PO A

, then find the locus of

P

. ii) Find the equation of locus of the point

Topic:

Coordinate Geometry

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Question 3

The orthocentre of the triangle

A BC

is '

B

' and the circumcentre is '

S

(a, b)

. If

A

is the origin, then the co-ordinates of

C

are :

$(2 a, 2 b)$
$(\frac{a}{2}, \frac{b}{2})$
$(a^{2} + b^{2}, 0)$
none

Topic:

Coordinate Geometry

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Question 4

7) In a class of 200 students who appeared certain examinations, 35 students failed in CET, 40 in NEET and 40 in JEE, 20 failed in CET and NEET, 17 in NEET and JEE, 15 in CET and JEE and 5 failed in all three examinations. Find how many students, i) did not fail in any examination. ii) failed in NEET or JEE entrance.

Topic:

Coordinate Geometry

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Question 5

\Rightarrow

Solve the following system of inequalities graphically

\Rightarrow 2 x + y \geq 6, 3 x + 4 y \leq 12

Topic:

Coordinate Geometry

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Question 6

4. The equation

a x^{2} + 2 h x y + b y^{2} + 2 gx + 2 f y + c = 0

, if the origion is to be shifted to eliminate

x, y

terms then the shifting point is 5.

(x_{1}, y_{1}) (x_{2}, y_{2})

are two vertices of equailateral triangle the third vertex

(x_{1} - x_{2})

Topic:

Coordinate Geometry

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Question 7

The value of a for which the lines represented by a are mutually perpendicular is

2
-2
25/8
none

Topic:

Co-ordinate Geometry

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Question 8

if p(x,y) is any point on the line passing through through a(x, y) b(x,y) then the ratio in which p divides ab is ap:pb=

Topic:

Coordinate Geometry

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Question 9

z) Solve the following system of inequalities graphically

x + y \geq 4, 2 x - y < 0

Topic:

Coordinate Geometry

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Question 10

a

and

b

, then find the value of

x

. 4. A.M of two numbers is 7 , their product is 45. Find the numbers. 5. A.M. berween two numbers is 6 . The sum of their squares is 90 . Find the numbers.

Topic:

Coordinate Geometry

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Question 11

20. Find the circumcentre of the triangle whose vertices are

(3, 8), (6, 11)

and

(9, 5)

. Find the radius of the circumcircle also.

Topic:

Coordinate Geometry

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Question 12

Parsing through

(2, 23)

and inclined with the

σ x \times

-axis at an angle of

7 5^{\circ}

Topic:

Coordinate Geometry

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Question 13

The acute angle

θ

through which the coordinate axes should be rotated for the point

A (2, 4)

to attain the new abscissa 4 is given by

$tan θ = 3/4$
$tan θ = 5/6$
$tan θ = 7/8$
$tan θ = 3/2$

Topic:

Coordinate Geometry

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Question 14

The maximum and minimum value of

y = 4 + 2 sin 0

respectively are :

4 and 0::. 6 and 2
6 and 0
4 and 2

Topic:

Coordinate Geometry

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Question 15

(i) equal in magnitude and both positive. (ii) equal in magnitude but opposite in sign. 4. For what values of

a

and

b

the intercepts cut off on the coordinate axes by the line

a x + b y + 8 = 0

are equal in length but opposite in signs to those cut off by the line

2 x - 3 y + 6 = 0

on the axes. [NCERT EXEMPLAR]

Topic:

Coordinate Geometry

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Question 16

The product of the perpendiculars from

(- 1, 2)

to the pair of lines

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

4
3
8
$5/2$

Topic:

Coordinate Geometry

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Question 17

ier is The centroid of an equilateral triangle is

(0, 0)

and length of the altitude is 9. The equation of the circumcircle is

$x^{2} + y^{2} = 6$
$x^{2} + y^{2} = 16$
$x^{2} + y^{2} = 9$
$x^{2} + y^{2} = 36$

Topic:

Coordinate Geometry

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Question 18

Vertices of a triangle are

(2, - 2), (- 2, 1), (5, 2)

. Find the distance between its Ortho-Centre and Centroid. (challenge sawaal)

Topic:

Coordinate Geometry

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Question 19

4 ab = 3 h^{2}

, then the ratio of slopes of the lines represented by the equation

a x^{2} + 2 h x y + b y^{2} = 0

will be

$2 : 1$
$2 : 1$
$3 : 1$
$1 : 3$

Topic:

Coordinate Geometry

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Question 20

742 Senior Secondary School Mathematics for Class 11 9. Find the equation of the parabola with vertex at the origin, passing through the point

P (5, 2)

and symmetric with respect to the

y

-axis. 10. Find the equation of the parabola which is symmetric about the

y

-axis and passes through the point

P (2, - 3)

. ANSWERS (EXERCISE 22) 1. (i)

F (3, 0), O (0, 0), x + 3 = 0, y = 0, 12

units

Topic:

Coordinate Geometry

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Co Ordinate Geometry - Mathematics Questions asked by Filo students

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