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If the equation 4x2 + ky2 = 18 represents a rectangular hyperbola, then k =
- a)4
- b)–4
- c)3
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If the equation 4x2 + ky2 = 18 represents a rectangular hyperbola, the...
We know that the equation
ax2 + by2 + 2hxy + 2gx + 2fy + c = 0
represent a rectangular hyperbola if Δ ≠ 0, h2 > ab and a + b = 0.
∴ The given equation represents a rectangular hyperbola if 4 + k = 0 i.e. k = -4
ax2 + by2 + 2hxy + 2gx + 2fy + c = 0
represent a rectangular hyperbola if Δ ≠ 0, h2 > ab and a + b = 0.
∴ The given equation represents a rectangular hyperbola if 4 + k = 0 i.e. k = -4
Most Upvoted Answer
If the equation 4x2 + ky2 = 18 represents a rectangular hyperbola, the...
To determine the value of k, we need to compare the given equation to the standard equation of a rectangular hyperbola, which is:
(x^2 / a^2) - (y^2 / b^2) = 1
In this equation, a represents the distance from the center to the vertices along the x-axis, and b represents the distance from the center to the vertices along the y-axis.
Comparing the given equation to the standard equation, we can see that a^2 = 4 and b^2 = 18. Therefore, a = 2 and b = √18.
Since the equation represents a rectangular hyperbola, a and b must be positive. So, b = √18 = 3√2.
Now, let's compare the values of a and b with the given options for k:
a) 4
b) 3√2
Since b = 3√2, the correct value of k is option b) 3√2.
(x^2 / a^2) - (y^2 / b^2) = 1
In this equation, a represents the distance from the center to the vertices along the x-axis, and b represents the distance from the center to the vertices along the y-axis.
Comparing the given equation to the standard equation, we can see that a^2 = 4 and b^2 = 18. Therefore, a = 2 and b = √18.
Since the equation represents a rectangular hyperbola, a and b must be positive. So, b = √18 = 3√2.
Now, let's compare the values of a and b with the given options for k:
a) 4
b) 3√2
Since b = 3√2, the correct value of k is option b) 3√2.
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If the equation 4x2 + ky2 = 18 represents a rectangular hyperbola, then k =a)4b)–4c)3d)none of theseCorrect answer is option 'B'. Can you explain this answer?
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If the equation 4x2 + ky2 = 18 represents a rectangular hyperbola, then k =a)4b)–4c)3d)none of theseCorrect answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If the equation 4x2 + ky2 = 18 represents a rectangular hyperbola, then k =a)4b)–4c)3d)none of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the equation 4x2 + ky2 = 18 represents a rectangular hyperbola, then k =a)4b)–4c)3d)none of theseCorrect answer is option 'B'. Can you explain this answer?.
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