QQ.The line 3y=4x -15 intersects the curve 8x2 = 45 + 27y2 at the points A & B. Find the coordinates of A and B.
Answers
Step-by-step explanation:
SOLUTION
GIVEN
The line 3y = 4x - 15 intersects the curve 8x² = 45 + 27y² at the points A & B.
TO DETERMINE
- The coordinates of A and B
EVALUATION
Here the given equation of the curve is
8x² = 45 + 27y² - - - - - - (1)
The given equation of the line is
3y = 4x - 15 - - - - (2)
For point of intersection we have
8x² = 45 + 3 × 9y²
⇒ 8x² = 45 + 3 × ( 4x - 15)²
⇒ 8x² = 45 + 48x² - 360x + 675
⇒ 40x² - 360x + 720 = 0
⇒ x² - 9x + 18 = 0
⇒ (x - 3)(x - 6) = 0
Now x - 3 = 0 gives x = 3
x - 6 = 0 gives x = 6
For x = 3 we get y = - 1
For x = 6 we have y = 3
So the points of intersections are
A (3, - 1) & B( 6,3)
FINAL ANSWER
Hence the required points are
A (3, - 1) & B ( 6,3)
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Answer:
x
2
+y
2
=4x+8y+5
x
2
+y
2
−4x−8y−5=0
(x−2)
2
+(y−4)−4−16−5=0
(x−2)
2
+(y−4)
2
=(5)
2
Therefore,
Centre of circle ≡(2,4)
Radius of circle =5
Given that the circle is intersecting the line 3x−4y=m at two distinct points.
Therefore,
Length of perpendicular < Radius of circle
3
2
+4
2
∣6−16−m∣
<5
5
∣m+10∣
<5
∣m+10∣<25
−25<m+10<25
−25−10<m<25−10
−35<m<15
Hence the correct answer is (B)−35<m<15.