Coordinate Geometry MCQs

1

Geometry • Coordinate Geometry

रेखा 3x + 2y = 12 निम्नलिखित में से किस बिंदु से होकर गुजरती है? The line 3x + 2y = 12 passes through which of the following points?

सेव करें Save सेव्ड Saved

A. (2, 3) (2, 3) B. (4, 1) (4, 1) C. (1, 6) (1, 6) D. (1, 4) (1, 4)

सही उत्तर: A Correct Answer: A

बिंदु (2, 3) रखने पर 3(2) + 2(3) = 6 + 6 = 12 प्राप्त होता है। इसलिए यह बिंदु दी गई रेखा पर स्थित है।

Substituting (2, 3) gives 3(2) + 2(3) = 12. Therefore, this point lies on the given line.

2

Geometry • Coordinate Geometry

D रेखाखंड AB का मध्यबिंदु है। यदि A और D के निर्देशांक क्रमशः (2, 4) और (-1, 3) हैं, तो B के निर्देशांक ज्ञात कीजिए। D is the midpoint of line segment AB. If the coordinates of A and D are (2, 4) and (-1, 3), respectively, find the coordinates of B.

सेव करें Save सेव्ड Saved

A. (3, 1) (3, 1) B. (-5, 4) (-5, 4) C. (-4, 2) (-4, 2) D. (4, -5) (4, -5)

सही उत्तर: C Correct Answer: C

मान लें B के निर्देशांक (x, y) हैं। मध्यबिंदु सूत्र से (2 + x)/2 = -1 और (4 + y)/2 = 3। इससे x = -4 तथा y = 2 प्राप्त होता है।

Let the coordinates of B be (x, y). Using the midpoint formula, (2 + x)/2 = -1 and (4 + y)/2 = 3. Thus, x = -4 and y = 2.

3

Geometry • Coordinate Geometry

Find the rectangular coordinates of the point with cylindrical coordinates (2, 2pi/3, 1). Find the rectangular coordinates of the point with cylindrical coordinates (2, 2pi/3, 1).

सेव करें Save सेव्ड Saved

A. (-1, sqrt(3), 1) (-1, sqrt(3), 1) B. (2, sqrt(3), -2) (2, sqrt(3), -2) C. (1, sqrt(3), 0) (1, sqrt(3), 0) D. (1, sqrt(3), -1) (1, sqrt(3), -1)

सही उत्तर: A Correct Answer: A

Using x = r cos(theta), y = r sin(theta), z = z, we get x = 2 cos(2pi/3) = -1, y = 2 sin(2pi/3) = sqrt(3), and z = 1.

4

Geometry • Coordinate Geometry

The Cartesian equation of the surface x = mu cos(nu), y = mu sin(nu), z = mu cot(nu) is: The Cartesian equation of the surface x = mu cos(nu), y = mu sin(nu), z = mu cot(nu) is:

सेव करें Save सेव्ड Saved

A. x^2 + z^2 = y^2 tan(nu) x^2 + z^2 = y^2 tan(nu) B. x^2 + y^2 = z^2 cot(nu) x^2 + y^2 = z^2 cot(nu) C. x^2 + y^2 = z^2 tan^2(nu) x^2 + y^2 = z^2 tan^2(nu) D. x^2 + z^2 = y^2 cot(nu) x^2 + z^2 = y^2 cot(nu)

सही उत्तर: C Correct Answer: C

From x^2 + y^2 = mu^2 and z = mu cot(nu), we have mu = z tan(nu). Therefore x^2 + y^2 = z^2 tan^2(nu).

5

Geometry • Coordinate Geometry

The equation x^2 - 6x + 6y + y^2 + 2 = 0 represents: The equation x^2 - 6x + 6y + y^2 + 2 = 0 represents:

सेव करें Save सेव्ड Saved

A. An ellipse with latus rectum 4 and focus at (-3,3) An ellipse with latus rectum 4 and focus at (-3,3) B. A circle with radius 4 and centre at (-3,3) A circle with radius 4 and centre at (-3,3) C. A circle with radius 4 and centre at (3,-3) A circle with radius 4 and centre at (3,-3) D. An ellipse with latus rectum 4 and focus at (3,-3) An ellipse with latus rectum 4 and focus at (3,-3)

सही उत्तर: C Correct Answer: C

Completing squares gives (x-3)^2 + (y+3)^2 = 16. This is a circle with centre (3,-3) and radius 4.

Coordinate Geometry MCQs

श्रेणी अनुसार अभ्यास करें

विषय अनुसार अभ्यास करें

टॉपिक अनुसार अभ्यास करें

परीक्षा अनुसार अभ्यास करें