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The gradient of the curve y – xy 2px 3qy = 0 at the point (3, 2 ) is -2 3 . The values of p and q are?
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The gradient of the curve y – xy 2px 3qy = 0 at the point (3, 2 ) ...
Given: The curve y - xy^2 + px + 3qy = 0 has a gradient of -2/3 at the point (3,2)
To find: The values of p and q
Explanation:
To find the values of p and q, we need to use the following formula:
Gradient of curve = -dy/dx = (2xy - y^2 + p)/(x - 3q)
We are given that the gradient of the curve at point (3,2) is -2/3. So we can substitute x=3 and y=2 in the above formula to get:
-2/3 = (2*3*2 - 2^2 + p)/(3 - 3q)
Simplifying the above equation, we get:
-2(3-3q) = 12 - 4 + 3(3-3q) + 2q
-6 + 6q = 15 - 9q + 2q
17q = 9
q = 9/17
Substituting the value of q in the above equation, we get:
-2/3 = (2*3*2 - 2^2 + p)/(3 - 3(9/17))
Simplifying the above equation, we get:
-2/3 = (8 + p)/(17/3)
Multiplying both sides by 17/3, we get:
-34/9 = 8 + p
p = -34/9 - 8
p = -106/9
Therefore, the values of p and q are -106/9 and 9/17 respectively.
To find: The values of p and q
Explanation:
To find the values of p and q, we need to use the following formula:
Gradient of curve = -dy/dx = (2xy - y^2 + p)/(x - 3q)
We are given that the gradient of the curve at point (3,2) is -2/3. So we can substitute x=3 and y=2 in the above formula to get:
-2/3 = (2*3*2 - 2^2 + p)/(3 - 3q)
Simplifying the above equation, we get:
-2(3-3q) = 12 - 4 + 3(3-3q) + 2q
-6 + 6q = 15 - 9q + 2q
17q = 9
q = 9/17
Substituting the value of q in the above equation, we get:
-2/3 = (2*3*2 - 2^2 + p)/(3 - 3(9/17))
Simplifying the above equation, we get:
-2/3 = (8 + p)/(17/3)
Multiplying both sides by 17/3, we get:
-34/9 = 8 + p
p = -34/9 - 8
p = -106/9
Therefore, the values of p and q are -106/9 and 9/17 respectively.
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The gradient of the curve y – xy 2px 3qy = 0 at the point (3, 2 ) is -2 3 . The values of p and q are?
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The gradient of the curve y – xy 2px 3qy = 0 at the point (3, 2 ) is -2 3 . The values of p and q are? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The gradient of the curve y – xy 2px 3qy = 0 at the point (3, 2 ) is -2 3 . The values of p and q are? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The gradient of the curve y – xy 2px 3qy = 0 at the point (3, 2 ) is -2 3 . The values of p and q are?.
The gradient of the curve y – xy 2px 3qy = 0 at the point (3, 2 ) is -2 3 . The values of p and q are? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The gradient of the curve y – xy 2px 3qy = 0 at the point (3, 2 ) is -2 3 . The values of p and q are? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The gradient of the curve y – xy 2px 3qy = 0 at the point (3, 2 ) is -2 3 . The values of p and q are?.
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