Maths-
General
Easy
Question
If the pair of lines
intersect on the x-axis, then ac=
- g2
- f2
- fg
- 2g2
Hint:
Put y=0 in the equation and then derive the expression.
The correct answer is: g2
Given That:
If the pair of lines
intersect on the x-axis, then ac=
>>> From unique point of intersection of pair of straight lines:
f2-bc=0 and g2-ac =0 when the pair of straight lines intersect at y-axis and x-axis respectively.
>>> Therefore, the given pair of straight lines intersect on the x-axis. Then,
g2 = ac .
>>>Therefore, the condition required is
.
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If the equation
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The transformed equation of
when the axes are rotated through an angle 36° is
>>> Given equation is x2+y2=r2. After rotation
>>> x=Xcos36∘−Ysin36∘ and y=Xsin36o+Ycos36∘
∴X2(cos236o+sin236o)+Y2(sin236o+cos236o)=r2
>>> ⇒X2+Y2=r2
The transformed equation of
when the axes are rotated through an angle 36° is
Maths-General
>>> Given equation is x2+y2=r2. After rotation
>>> x=Xcos36∘−Ysin36∘ and y=Xsin36o+Ycos36∘
∴X2(cos236o+sin236o)+Y2(sin236o+cos236o)=r2
>>> ⇒X2+Y2=r2
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When axes rotated an angle of
the transformed form of
is
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the transformed form of
is
maths-General
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The transformed equation of
when the axes are rotated through an angle 90° is
>>> Therefore, the equation becomes =1.
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when the axes are rotated through an angle 90° is
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maths-
The arrangement of the following in ascending order of angle to eliminate xy term in the following equations
A) 
B) 
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The angle of rotation of axes to remove xy term of the equation
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Angle of rotation will be 45 degrees.
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The angle of rotation of axes in order to eliminate xy term of the equation
is
The Angle of rotation becomes
The angle of rotation of axes in order to eliminate xy term of the equation
is
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The Angle of rotation becomes