Question

5. Find two different equation of straight lines which passes through the point (4, 5)
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Answer 1

Answer:

Find the equation of a straight line passing through the point (4,5) and equally inclined to the lines 3x=4y+7 and 5y=12x+6.

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Step-by-step explanation:

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ANSWER

Let the Slope of line be m

Now, slope of other lines are

43 , 512

The Slope is Equally inclined so it must lie between these slopes

such that 43

<m<

5

12

As it is equally inclined so angle between the line and the two given line must be same

⇒θ

1

=θ

2

⇒tanθ

1

=tanθ

2

⇒

1+

5

12

m

5

12

−m

=

1+

4

3

m

m−

4

3

⇒63m

2

−32m−63=0

⇒m=

2∗63

32±

32

2

+4∗63∗63

⇒m=

9

−7

,

7

9

Now, Equation of line as it passes through (4,5) will be

y−5=m(x−4)

Putting the obtained values of m in above Equation we get

9x−7y=1

7x+9y=73