Question

O(0,0) , A(1,2), B(3,4) are the vertices of a triangle OAB. The joint equation of the altitude and median drawn from O is.......... ?
a)
${x}^{2} + xy - {y}^{2} = 0$
b)
${x}^{2} + 7xy + {y}^{2} = 0$
c)
$3 {x}^{2} - xy - 2 {y}^{2} = 0$
d)
$3 {x}^{2} + xy - 2 {y}^{2} = 0$
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Answer 1

Answer:

d)3x^2 + xy − 2y^2 = 0

Step by step explanation:

Equation of median OD=y=mx⇒3=2m

⇒m= 3/2

∴y= 3x/2 ⇒3x−2y=0

Slope of AB= 2/2 =1⇒ Slope of OP=−1

Equation of OP⇒y=−x⇒x+y=0

Joint equation of OP and OD⇒(x+y)(3x−2y)=0

⇒3x^2 + xy −2y^2 = 0