Let two lines be intersecting at 4-3 and angle between them is 45- If the slope of one line is 2- then the equation of the other line can be

Let slope of required line =m ⇒tan45^∘= | m 21+2m | ⇒1= | m 21+2m | ⇒1+2m=± (m 2) ⇒ m= 3, 13 Now, the line passes through (4,3). Then the equation of the line ...

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Standard XIII

Mathematics

Angle between Two Lines

Let two lines...

Question

Let two lines be intersecting at $(4, 3)$ and angle between them is $45^{\circ} .$ If the slope of one line is $2,$ then the equation of the other line can be

3 x - y - 9 = 0

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3 x + y - 15 = 0

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x - 3 y + 5 = 0

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x + 3 y - 13 = 0

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Solution

The correct option is C $x - 3 y + 5 = 0$
Let slope of required line $= m$
$\Rightarrow tan 45^{\circ} = ∣ ∣ ∣ \frac{m - 2}{1 + 2 m} ∣ ∣ ∣ \Rightarrow 1 = ∣ ∣ ∣ \frac{m - 2}{1 + 2 m} ∣ ∣ ∣ \Rightarrow 1 + 2 m = \pm (m - 2) \Rightarrow m = - 3, \frac{1}{3}$

Now, the line passes through $(4, 3) .$
Then the equation of the line is
$y - 3 = - 3 (x - 4)$ or $y - 3 = \frac{1}{3} (x - 4)$
$\Rightarrow 3 x + y - 15 = 0$ or $x - 3 y + 5 = 0$

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Let two lines be intersecting at (4,3) and angle between them is 45∘. If the slope of one line is 2, then the equation of the other line can be

The correct option is C x−3y+5=0Let slope of required line =m ⇒tan45∘=∣∣∣m−21+2m∣∣∣⇒1=∣∣∣m−21+2m∣∣∣⇒1+2m=±(m−2)⇒m=−3,13 Now, the line passes through (4,3). Then the equation of the line is y−3=−3(x−4) or y−3=13(x−4) ⇒3x+y−15=0 or x−3y+5=0

Let two lines be intersecting at $(4, 3)$ and angle between them is $45^{\circ} .$ If the slope of one line is $2,$ then the equation of the other line can be