Download App

The Straight Lines — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSThe Straight Lines3 Marks
Question
Find the equation to the straight line which passes through the point (5, 6) and has intercepts on the axes Equal in magnitude and both positive,Equal in magnitude but opposite in sign.
✓

Answer

Intercepts are equal positive⇒ a = b = k
The equation of straight line is
$\frac{\text{x}}{\text{a}}+\frac{\text{y}}{\text{b}}=1 \ ...(\text{i})$
Since this line passes through (5, 6) and a = b = k, we get:
$\frac{5}{\text{k}}+\frac{6}{\text{k}}=1$
$\text{k}=1$
$\therefore\frac{\text{x}}{11}+\frac{\text{y}}{11}=1$
$\Rightarrow\text{x}+\text{y}=11$
Intercepts are equal but opposite in sing
Let, a = k, b = -k
Putting in (i), we get,
$\frac{5}{\text{k}}+\frac{6}{-\text{k}}=1$
$\frac{5}{\text{k}}-\frac{6}{\text{k}}=1$
$\Rightarrow\text{k}=-1$
thus from (i)
$\text{x}-\text{y}=-1$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "(Each question 3 marks)" from The Straight Lines→The Straight Lines — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow3}\big(\text{x}^2-9\big)\Big(\frac{1}{\text{x}+3}-\frac{1}{\text{x}-3}\Big)$
→
Find the conjugates of the following complex numbers: $\frac{1}{3+5\text{i}}$
→
m men and n women are to be seated in a row so that no two women sit together, if m > n then show that the number of ways in which they can be seated as $\frac{\text{m}! (\text{m}+1)!(\text{m}−\text{n}+1)!}{\text{m}! (\text{m}+1)!(\text{m}-\text{n}+1) !}$
→
If $x - iy = \sqrt {\frac{{a - ib}}{{c - id}}} $ prove that ${({x^2} + {y^2})^2} = \frac{{{a^2} + {b^2}}}{{{c^2} + {d^2}}}$
→
Find the modulus and argument of the following complex numbers and hence express each of them in the polar form: $\frac{1}{1+\text{i}}$
→
Differentiate the following function with respect to x:$\text{x}^{-3}(5+\text{3x})$
→
Solve the following system of equations in R. $\Big|\text{x}+\frac{1}{3}\Big|>\frac{8}{3}$
→
A man wants to cut three lengths from a single piece of board of length 91cm. The second length is to be 3cm longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths of the shortest board if the third piece is to be at least 5cm longer than the second?
[Hint: If x is the length of the shortest board, then x , (x + 3) and 2x are the lengths of the second and third piece, respectively. Thus, x + (x + 3) + 2x $\leq$ 91 and 2x $\ge$ (x + 3) + 5].
→
Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
$\frac{{{x^2}}}{{100}} + \frac{{{y^2}}}{{400}} = 1$
→
If ${ }^n C_{10}={ }^n C_{12}$, Find ${ }^{23} C_n$.
→