# Let a tangent to any curve at a point P on it cuts $x-axis$ at N. If a & b are lenght of subtangent and subnormal then a + b equals ? Option 1) $PT + PN$ Option 2) $\sqrt{PT^2 + PN^2}$ Option 3) $PT\cdot PN$ Option 4) $\sqrt{PT\cdot PN}$

H Himanshu

As we have learned

Concept of sub Tangent and sub Normal -

When Tangent and Normal cuts the x-axis at a point and perpendicular from point of contact to x-axis.Then this is sub Normal & Tangent.From fig TS  and SN are known as sub tangent and sub normal.

- wherein

$(a+b)^{2}= (PT)^{2}+(PN)^{2}$

$(a+b)= \sqrt{(PT)^{2}+(PN)^{2}}$

Option 1)

$PT + PN$

Option 2)

$\sqrt{PT^2 + PN^2}$

Option 3)

$PT\cdot PN$

Option 4)

$\sqrt{PT\cdot PN}$

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