let P be (m,n). parametric eq of line through P is

x=rcos(A)+m, y=rsin(A)+n

solving with the given curve

a(rcos(A)+m)²  + b(sin(A)+n)² +2h(rcos(A)+m)(rsin(A)+N) -1=0

frm this we get

PQ.PR=mod(r₁)mod(r₂)=mod(am²+bn²+2hmn-1)/(acos²(A) + asin²(A) - hsin(2A))..........(1)

if PQ.PR is constant then as the numerator in eq (1) is const. the denominator will also be const.

i.e. acos²(a)+bsin²(A) - hsin(2A) must be a constant for all values of (A) ....let that const be C.....

put (A)=o...we get a=C

(A)=90^o....we get b=C

frm the abv eqtns we get  .......a=b.......(2)

substituting (2) in the denominator of eq 1we get

a-hsin(2A)=C

but a=C

so it gives hsin(2A)=0......or h=0............(3)

hence it is a circle from eq (2) and (3)

use hot  it can also be used to convert any bulky alkyl grp to benzoic acid

due to the small size of the e- cloud is denser in it than in the other given ions so the greater availability of e- makes it a better nucleophile

helloo... sorry dude but in benzene each carbon is sp2 hybridized with a bond angle 120.

among the 3sp2 hyb orbitals 2 of 'em overlaps with another 2 sp2 hyb orbitals of  other two diff c atoms and one with the s orbital of hydrogen......the left unhybridized p orbital does lateral overlaping to form bonds

Inductive effect is of two types +I and -I

in +I effect  take C-Y where y is an electropositive element or group the e- pair will be somewhat displaced towards C giving  it a slight -ve charge.

-I can be seen in C-X type of bonds where e- pair is shifted towards X which is more electronegetive

in short it can be said that if inan organic compound the carbon chain is rendered +ve due to a particular group the group shows -I effect and if  -ve it shows +I effect

The inductive effect causes certain degree of polarity in the bond which in turn renders the bond much more liable to be attacked by charged atoms or groups. 

in a covalent bond between two atoms having a large difference in electronegetivity , the electron pair shared b/w de atoms is shifted slightly towards the more electronegetive atom of the two. ex-in C-X bond the e- pair is shifted towards x atom and as a result it attains apartial -ve charge and c attains a partial +ve charge .