Math, asked by sumanpal43, 2 months ago

find the values of h and k.
11. Find the distance of the line 3x + y + 4 = 0 from the point
(2,5) measured parallel to the line 3x – 4y + 8 = 0.​

Answers

Answered by saranyab620
0

Step-by-step explanation:

Let distance be 'r'.

Co-ordinates of 'P' are

(2+rcosθ,5+rsinθ) where tanθ=

4

3

which lies on the line 3x+y+4=0

3(2+rcosθ)+5+rsinθ+4=0

r(3.

5

4

+

5

3

)+15=0⇒r=−

3

15

=−5

But distance can not be negative

∴r=5

Answered by soumaryasoumalya12
0

Answer:

As shown in the figure, let P (2,5) = () be the point from which we are measuring the distance .

The equation of the line passing through the point P and having slope  is,

4y-20=3x-6

3x-4y+14=0                   (1)

Now, at point A, let this line intersect the given line 3x+y+4=0     (2)

therefore the required distance will be AP.

Subtracting equation (2) from (1)

3x-4y+14-(3x+y+4)=0

3x-4y+14-3x-y-4=0

-5y+10=0

5y=10

y=2

substitute the value of y in equation (2)

3x+y+4=0

3x+2+4=0

3x+6=0

3x=-6

 

x=-2

Therefore the co-ordinates of the point A is (-2,2). and we have P (2,5).

Distance,

AP=5

Hence AP= 5 units.

Step-by-step explanation:

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