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
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
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: