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A and B are any two points on the + X axis and Y axis respectively satisfying 2(OA)+3(OB)=10.If P is the middle point of AB then the locus of P is:-?
Most Upvoted Answer
A and B are any two points on the + X axis and Y axis respectively sat...
Explanation:
Given, A and B are any two points on the X axis and Y axis respectively satisfying 2(OA) 3(OB)=10.
Let the coordinates of A be (a,0) and B be (0,b).
Then, using the distance formula, we have OA = |a| and OB = |b|.
Substituting these values in the given equation, we get:
2|a| + 3|b| = 10
Simplifying, we get:
|a|/5 + |b|/(10/3) = 1
This is the equation of an ellipse with semi-axes a/5 and b/(10/3).
The center of the ellipse is (0,0) and the major axis is along the x-axis.
Now, let P be the midpoint of AB, i.e. P = ((a+0)/2, (0+b)/2) = (a/2, b/2).
Thus, the locus of P is the locus of the midpoint of a line segment joining a point on the x-axis to a point on the y-axis, which is the interior of the ellipse.
Therefore, the locus of P is an ellipse with semi-axes a/10 and b/(20/3), centered at the origin.
Given, A and B are any two points on the X axis and Y axis respectively satisfying 2(OA) 3(OB)=10.
Let the coordinates of A be (a,0) and B be (0,b).
Then, using the distance formula, we have OA = |a| and OB = |b|.
Substituting these values in the given equation, we get:
2|a| + 3|b| = 10
Simplifying, we get:
|a|/5 + |b|/(10/3) = 1
This is the equation of an ellipse with semi-axes a/5 and b/(10/3).
The center of the ellipse is (0,0) and the major axis is along the x-axis.
Now, let P be the midpoint of AB, i.e. P = ((a+0)/2, (0+b)/2) = (a/2, b/2).
Thus, the locus of P is the locus of the midpoint of a line segment joining a point on the x-axis to a point on the y-axis, which is the interior of the ellipse.
Therefore, the locus of P is an ellipse with semi-axes a/10 and b/(20/3), centered at the origin.
Community Answer
A and B are any two points on the + X axis and Y axis respectively sat...
2x+3y=5. OA is distance from (0,0) to A on xaxis so let OA= x. OB is distance from (0,0) to B on yaxis OB =y.
p=(x/2,y/2).
let p= (a,b).
a=2x,b=2y.
since p lies on eq 2x+2y=10 ie 2OA+2OB=10.
Now , 2*2x+2*2y=10.
2x+2y=5
p=(x/2,y/2).
let p= (a,b).
a=2x,b=2y.
since p lies on eq 2x+2y=10 ie 2OA+2OB=10.
Now , 2*2x+2*2y=10.
2x+2y=5
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A and B are any two points on the + X axis and Y axis respectively satisfying 2(OA)+3(OB)=10.If P is the middle point of AB then the locus of P is:-?
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A and B are any two points on the + X axis and Y axis respectively satisfying 2(OA)+3(OB)=10.If P is the middle point of AB then the locus of P is:-? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A and B are any two points on the + X axis and Y axis respectively satisfying 2(OA)+3(OB)=10.If P is the middle point of AB then the locus of P is:-? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A and B are any two points on the + X axis and Y axis respectively satisfying 2(OA)+3(OB)=10.If P is the middle point of AB then the locus of P is:-?.
A and B are any two points on the + X axis and Y axis respectively satisfying 2(OA)+3(OB)=10.If P is the middle point of AB then the locus of P is:-? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A and B are any two points on the + X axis and Y axis respectively satisfying 2(OA)+3(OB)=10.If P is the middle point of AB then the locus of P is:-? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A and B are any two points on the + X axis and Y axis respectively satisfying 2(OA)+3(OB)=10.If P is the middle point of AB then the locus of P is:-?.
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