>
Exams
>
Mathematics
>
Conic sections
>
equation frac 1 r frac 1 8 frac 3 8 cos theta repr
Question:
Equation $\frac{1}{r}=\frac{1}{8}+\frac{3}{8} cos\, \theta represents$
VITEEE - 2017
VITEEE
Updated On:
Feb 15, 2025
A rectangular hyperbola
A hyperbola
An ellipse
A parabola
Hide Solution
Verified By Collegedunia
The Correct Option is
B
Solution and Explanation
Given, equation is $\frac{1}{r}=\frac{1}{8}+\frac{3}{8} cos \theta \, or\, \frac{8}{r}=1+3 cos \theta$ which is the form of $\frac{l}{r}=1+ e \, cos\, \theta$ $\because\quad e=3 >\, 0, $ $\therefore\quad Given \, equation \,is \,a \,hyperbola.$
Download Solution in PDF
Was this answer helpful?
0
0
Top Questions on Conic sections
Let \(A\) be the focus of the parabola \(y^2=8x\). Let the line \(y=mx+c\) intersect the parabola at two distinct points \(B\) and \(C\). If the centroid of triangle \(ABC\) is \(\left(\frac{7}{3},\frac{4}{3}\right)\), then \((BC)^2\) is equal to:
JEE Main - 2026
Mathematics
Conic sections
View Solution
Let f be a twice differentiable non-negative function such that \((f(x))^2 = 25 + \int_0^x ( f(t)^2 + (f'(t))^2 ) dt\). Then the mean of \(f(\log_2(1)), f(\log_2(2)), \dots, f(\log_2(625))\) is equal to :
JEE Main - 2026
Mathematics
Conic sections
View Solution
For some \( \theta\in\left(0,\frac{\pi}{2}\right) \), let the eccentricity and the length of the latus rectum of the hyperbola \[ x^2-y^2\sec^2\theta=8 \] be \( e_1 \) and \( l_1 \), respectively, and let the eccentricity and the length of the latus rectum of the ellipse \[ x^2\sec^2\theta+y^2=6 \] be \( e_2 \) and \( l_2 \), respectively. If \[ e_1^2=\frac{2}{e_2^2}\left(\sec^2\theta+1\right), \] then \[ \left(\frac{l_1l_2}{e_1^2e_2^2}\right)\tan^2\theta \] is equal to:
JEE Main - 2026
Mathematics
Conic sections
View Solution
Let \( \vec{c} \) and \( \vec{d} \) be vectors such that \[ |\vec{c} + \vec{d}| = \sqrt{29} \] and \[ \vec{c} \times (2\hat{i} + 3\hat{j} + 4\hat{k}) = (2\hat{i} + 3\hat{j} + 4\hat{k}) \times \vec{d}. \] If \( \lambda_1, \lambda_2 \) (\( \lambda_1 > \lambda_2 \)) are the possible values of \[ (\vec{c} + \vec{d}) \cdot (-7\hat{i} + 2\hat{j} + 3\hat{k}), \] then the equation \[ K^2 x^2 + (K^2 - 5K + \lambda_1)xy + \left(3K + \frac{\lambda_2}{2}\right)y^2 - 8x + 12y + \lambda_2 = 0 \] represents a circle, for \( K \) equal to
JEE Main - 2026
Mathematics
Conic sections
View Solution
Let \( P(10, 2\sqrt{15}) \) be a point on the hyperbola \[ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1, \] whose foci are \( S \) and \( S' \). If the length of its latus rectum is \(8\), then the square of the area of \( \triangle PSS' \) is equal to
JEE Main - 2026
Mathematics
Conic sections
View Solution
View More Questions
Questions Asked in VITEEE exam
Find the value of \( x \) in the following equation:
\[ \frac{2}{x} + \frac{3}{x + 1} = 1 \]
VITEEE - 2025
Algebra
View Solution
How many numbers between 0 and 9 look the same when observed in a mirror?
VITEEE - 2025
Odd one Out
View Solution
In a code language, 'TIGER' is written as 'JUISF'. How will 'EQUAL' be written in that language?
VITEEE - 2025
Odd one Out
View Solution
In a code language, 'TIGER' is written as 'JUISF'. How will 'EQUAL' be written in that language?
VITEEE - 2025
Data Interpretation
View Solution
TUV : VYB :: PRA : ?
VITEEE - 2025
Odd one Out
View Solution
View More Questions