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The position of the point (1, 2) relative to the ellipse 2x2 + 7y2 = 20 is
- a)Outside the ellipse
- b)Inside the ellipse but not at the focus
- c)On the ellipse
- d)At the focus
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The position of the point (1, 2) relative to the ellipse 2x2 + 7y2 = 2...
2(1)2 + 7(2)2 − 20 = 2 + 28 − 20 > 0
∴ point lies outside the ellipse.
∴ point lies outside the ellipse.
Most Upvoted Answer
The position of the point (1, 2) relative to the ellipse 2x2 + 7y2 = 2...
The Position of Point (1, 2) Relative to the Ellipse 2x^2 + 7y^2 = 20
To determine the position of the point (1, 2) relative to the ellipse 2x^2 + 7y^2 = 20, we need to analyze the equation of the ellipse and compare it to the coordinates of the point.
Equation of the Ellipse:
The equation of the ellipse is given as 2x^2 + 7y^2 = 20. We can rewrite this equation in terms of x and y to get a better understanding of its shape and properties.
Dividing both sides of the equation by 20, we have:
x^2/10 + y^2/(20/7) = 1
This equation represents an ellipse centered at the origin (0, 0) with semi-major axis a = √10 and semi-minor axis b = √(20/7).
Position of the Point (1, 2):
The point (1, 2) has coordinates x = 1 and y = 2.
Comparing the Coordinates with the Equation:
To determine the position of the point relative to the ellipse, we substitute the coordinates (x, y) = (1, 2) into the equation of the ellipse and evaluate the equation.
Substituting x = 1 and y = 2 into the equation, we have:
(1^2)/10 + (2^2)/(20/7) = 1/10 + 4/(20/7) = 1/10 + 4*(7/20) = 1/10 + 7/5 = 1/10 + 14/10 = 15/10 = 3/2
The value of the equation is 3/2, which is greater than 1.
Interpretation:
Since the value of the equation is greater than 1, the point (1, 2) is outside the ellipse.
Therefore, the correct answer is option 'A': Outside the ellipse.
To determine the position of the point (1, 2) relative to the ellipse 2x^2 + 7y^2 = 20, we need to analyze the equation of the ellipse and compare it to the coordinates of the point.
Equation of the Ellipse:
The equation of the ellipse is given as 2x^2 + 7y^2 = 20. We can rewrite this equation in terms of x and y to get a better understanding of its shape and properties.
Dividing both sides of the equation by 20, we have:
x^2/10 + y^2/(20/7) = 1
This equation represents an ellipse centered at the origin (0, 0) with semi-major axis a = √10 and semi-minor axis b = √(20/7).
Position of the Point (1, 2):
The point (1, 2) has coordinates x = 1 and y = 2.
Comparing the Coordinates with the Equation:
To determine the position of the point relative to the ellipse, we substitute the coordinates (x, y) = (1, 2) into the equation of the ellipse and evaluate the equation.
Substituting x = 1 and y = 2 into the equation, we have:
(1^2)/10 + (2^2)/(20/7) = 1/10 + 4/(20/7) = 1/10 + 4*(7/20) = 1/10 + 7/5 = 1/10 + 14/10 = 15/10 = 3/2
The value of the equation is 3/2, which is greater than 1.
Interpretation:
Since the value of the equation is greater than 1, the point (1, 2) is outside the ellipse.
Therefore, the correct answer is option 'A': Outside the ellipse.
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