write an equation of a line which coincides with 4x+5y=10
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Given joint equation of lines is
ax2+2hxy+by2=0
∴ It's auxilary equation is
bm2+2hm+a=0 ______ (i)
One of the line is 4x+5y=0
∴ slope = 5−4=m
Now, −4/5 must be one of the roots of the auxilary equation (i)
∴b(−4/5)2+2b(−4/5)+a=0
b(16/25)+2h(−4/5)+a=0
multiplying both sides of equation by 25
∴16b−40h+25a=0
∴25a−40b+16=0
Hence proved
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hence prove
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