Conic Sections MCQs

1

Mathematics • Conic Sections

For what value of m is the line y = mx + 5 tangent to the ellipse represented by 4x^2/9 + y^2/16 = 1? For what value of m is the line y = mx + 5 tangent to the ellipse represented by 4x^2/9 + y^2/16 = 1?

A. 2 2 B. plus or minus 2 plus or minus 2 C. plus or minus 3 plus or minus 3 D. 3 3

सही उत्तर: B Correct Answer: B

For y = mx + c to be tangent to x^2/a^2 + y^2/b^2 = 1, c^2 = a^2m^2 + b^2. Here a^2 = 9/4, b^2 = 16 and c = 5, giving m^2 = 4, so m = plus or minus 2.

2

Mathematics • Conic Sections

Find the focus of the conic x^2 + 19 - 8x - y = 0. Find the focus of the conic x^2 + 19 - 8x - y = 0.

A. (4, 3.25) (4, 3.25) B. (2.75, 4) (2.75, 4) C. (3.25, 4) (3.25, 4) D. (4, 2.75) (4, 2.75)

सही उत्तर: A Correct Answer: A

Rewriting gives (x - 4)^2 = y - 3. Comparing with (x-h)^2 = 4a(y-k), we get a = 1/4, so the focus is (4, 3 + 1/4) = (4, 3.25).

3

Mathematics • Conic Sections

For the conic r = 1 + sin(omega), the slope of the tangent to the conic at omega = pi/3 is: For the conic r = 1 + sin(omega), the slope of the tangent to the conic at omega = pi/3 is:

A. -1/2 -1/2 B. 1/2 1/2 C. -1 -1 D. 1 1

सही उत्तर: C Correct Answer: C

For a polar curve, dy/dx = (r' sin(omega) + r cos(omega))/(r' cos(omega) - r sin(omega)), where r' here denotes dr/domega. Substituting r = 1 + sin(omega) at omega = pi/3 gives -1.

4

Mathematics • Conic Sections

For what value of c is the line y=0.5x+c tangent to the parabola y^2=4ax? For what value of c is the line y=0.5x+c tangent to the parabola y^2=4ax?

A. a/2 a/2 B. a/4 a/4 C. 2a 2a D. a a

सही उत्तर: C Correct Answer: C

A tangent to y^2=4ax with slope m has equation y=mx+a/m. With m=0.5, the intercept is c=a/0.5=2a.

5

Mathematics • Conic Sections

Which conic does the equation R=5/(4-11cos(omega)) represent? Which conic does the equation R=5/(4-11cos(omega)) represent?

A. Hyperbola Hyperbola B. Parabola Parabola C. Ellipse Ellipse D. Circle Circle

सही उत्तर: A Correct Answer: A

Writing the denominator in standard polar-conic form shows eccentricity e=11/4. Since e>1, the conic is a hyperbola.

Conic Sections MCQs

श्रेणी अनुसार अभ्यास करें

विषय अनुसार अभ्यास करें

टॉपिक अनुसार अभ्यास करें

परीक्षा अनुसार अभ्यास करें